RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3

RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Linear Equations in One Variable Ex 9.3

Other Exercises

Solve the following equations and verify your answer :
Question 1.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 1
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 2

Question 2.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 3
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 4
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 5

Question 3.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 6
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 7

Question 4.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 8
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 9
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 10

Question 5.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 11
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 12

Question 6.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 13
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 14
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 15

Question 7.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 16
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 17

Question 8.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 18
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 19

Question 9.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 20

Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 21
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 22

Question 10.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 23
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 24
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 25

Question 11.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 26
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 27

Question 12.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 28
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 29
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 30
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 31

Question 13.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 32
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 33
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 34
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 35

Question 14.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 36
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 37
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 38
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 39

Question 15.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 40
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 41
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 42

Question 16.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 43
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 44
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 45

Question 17.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 46
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 47

Question 18.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 48
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 49
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 50

Question 19.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 51
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 52

Question 20.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 53
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 54
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 55
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 56

Question 21.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 57
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 58
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 59

Question 22.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 60
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 61
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 62

Question 23.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 63
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 64
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 65
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 66

Question 24.
Find a positive value of x for which the given equation is satisfied.
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 67
Solution:
RD Sharma Class 8 Solutions Chapter 9 Linear Equations in One Variable Ex 9.3 68

Hope given RD Sharma Class 8 Solutions Linear Equations in One Variable Ex 9.3 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13D

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13D

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13D.

Other Exercises

Objective questions
Mark against the correct answer in each of following.

Question 1.
Solution:
(c) vertex of an angle lie on it.

Question 2.
Solution:
(c) an angle.

Question 3.
Solution:
(c) A straight angle has 180°

Question 4.
Solution:
An angle measuring 90° is called a right angle. (b)

Question 5.
Solution:
An angle measuring 91° is an obtuse angle as it is more than 90° and less than 180°.(b)

Question 6.
Solution:
An angle measuring 270° is a reflex angles as it is greater than 180° and less than 360°. (d)

Question 7.
Solution:
(c) A straight angle is equal to 180°

Question 8.
Solution:
(c) A reflex angles is greater than 180° but less than 360°

Question 9.
Solution:
(d) A complete angle is equal to 360°.

Question 10.
Solution:
(b) A reflex angle is greater than 180° but less than 360°.

Question 11.
Solution:
Two right angles = (2 x 90)°
= 180° (b)

Question 12.
Solution:
\(\frac { 3 }{ 2 } \) of a right angle = \(\frac { 3 }{ 2 } \) x 90° = 135° as 1 right angle = 90° (b)

Question 13.
Solution:
36 spokes has 360°
Angle between two adjacent spokes
= \(\frac { { 360 }^{ O } }{ { 36 }^{ O } } \) = 10° (c)

Hope given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13D are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness)

Number System Exercise 1A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Which is greater?
(i) 537 or 98
(ii) 2428 or 529
(iii) 2, 59, 467 or 10, 35, 729
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 1

Question 2.
Which is smaller?
(i) 428 or 437
(ii) 2497 or 2597
(iii) 3297 or 3596
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 2

Question 3.
Which is greater?
(i) 45293 or 45427
(ii) 380362 or 381007
(iii) 63520 or 63250
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 3

Question 4.
By making a suitable chart, compare:
(i) 540276 and 369998
(ii) 6983245 and 6893254
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 4

Question 5.
Compare the numbers written in the following table by writing them in ascending order:

5 4 3 2 9 7 2
2 3 1 0 6 2 9 3
5 2 2 3 7 9 1
2 3 1 8 2 6 3 4
5 4 3 4 4 7 8 2

Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 5

Question 6.
Use table form to compare the numbers in descending order : 5,43,287; 54,82,900; 27,32,940; 43,877 ; 78,396 and 4,999
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 6

Question 7.
Find the smallest and the greatest numbers in each case given below:
(i) 983, 5754, 84 and 5942
(ii) 32849, 53628, 5499 and 54909.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 7

Question 8.
Form the greatest and the smallest 4 digit numbers using the given digits without repetition
(i) 3, 7, 2 and 5
(ii) 6, 1, 4 and 9
(iii) 7, 0, 4 and 2
(iv) 1, 8, 5 and 3
(v) 9, 6, 0 and 7
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 8

Question 9.
Form the greatest and the smallest 3-digit numbers using any three different digits with the condition that digit 6 is always at the unit (one’s) place.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 9

Question 10.
Form the greatest and the smallest 4-digit number using any four different digits with the condition that digit 5 is always at ten’s place.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 10

Question 11.
Fill in the blanks :
(i) The largest number of 5-digit is …………… and the smallest number of 6-digit is …………….
(ii) The difference between the smallest number of four digits and the largest number of three digits = …………. – ………….. = …………..
(iii) The sum (addition) of the smallest number of three digit and the largest number of two digit = ………… + …………= ………….
(iv) On adding one to the largest five digit number, we get ……………. which is the smallest ……………… digit number.
(v) On subtracting one from the smallest four digit number, we get ……………… which is the ……………. three digit number.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 11

Question 12.
Form the largest number with the digits 2, 3, 5, 9, 6 and 0 without repetition of digits.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 12

Question 13.
Write the smallest and the greatest numbers of 4 digits without repetition of any digit.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 13

Question 14.
Find the greatest and the smallest five digit numbers with 8 in hundred’s place and with all the digits different.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 14

Question 15.
Find the sum of the largest and the smallest four-digit numbers:
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 15

Question 16.
Find the difference between the smallest and the greatest six-digits numbers.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 16

Question 17.
(i) How many four digit numbers are there between 999 and 3000?
(ii) How many four digit numbers are there between 99 and 3000?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 17

Question 18.
How many four digit numbers are there between 500 and 3000?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 18

Question 19.
Write all the possible three digit numbers using the digits 3, 6 and 8 only; if the repetition of digits is not allowed.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 19

Question 20.
Make the greatest and the smallest 4-digit numbers using the digits 5, 4, 7 and 9 (without repeating the digits) and with the condition that:
(i) 7 is at unit’s place.
(ii) 9 is at ten’s place
(iii) 4 is at hundred’s place
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 20
(i) 7 is at unit’s place

Number System Exercise 1B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Population of a city was 3, 54, 976 in the year 2014. In the year 2015, it was found to be increased by 68, 438. What was the population of the city at the end of the year 2015?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 21

Question 2.
A = 7,43,000 and B = 8,00,100. Which is greater A or B ? And, by how much?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 22

Question 3.
A small and thin notebook has 56 pages. How many total numbers of pages will 5326 such note-books have?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 23

Question 4.
The number of sheets of paper available for making notebooks is 75,000. Each sheet makes 8 pages of a notebook. Each notebook contains 200 pages. How many notebooks can be made from the available paper?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 24

Question 5.
Add 1, 76, 209; 4, 50, 923 and 44, 83, 947
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 25

Question 6.
A cricket player has so far scored 7, 849 runs in test matches. He wishes to complete 10, 000 runs ; how many more runs does he need?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 26

Question 7.
In an election two candidates A and B are the only contestants. If candidate A scored 9, 32, 567 votes and candidates B scored 9, 00, 235 votes, by how much margin did A win or loose the election?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 27

Question 8.
Find the difference between the largest and the smallest number that can be written using the digits 5, 1, 6,3 and 2 without repeating any digit.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 28

Question 9.
A machine manufactures 5,782 screws every day. How many screws will it manufacture in the month of April ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 29

Question 10.
A man had ₹ 1, 57, 184 with him. He placed an order for purchasing 80 articles at 125 each. How much money will remain with him after the purchase?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 30

Question 11.
A student multiplied 8,035 by 87 instead of multiplying by 78. By how much was his answer greater than or less than the correct answer?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 31

Question 12.
Mohani has 30 m cloth and she wants to make some shirts for her son. If each shirt requires 2 m 30 cm cloth, how many shirts, in all, can be made and how much length of cloth will be lefft?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 32

Question 13.
The weight of a box is 4 kg 800 gm. What is the total weight of 150 boxes?>
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 33

Question 14.
The distance between two places A and B is 3 km 760 m. A boy travels A to B and then B to A every day. How much distance does he travel in 8 days?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 34

Question 15.
An oil-tin contains 6 litre 60 ml oil. How many identical bottles can the oil fill, if capacity of each bottle is 30 ml ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 35

Question 16.
The scale receipt of a company in a certain year was ₹ 83, 73, 540. In the following year, it was decreased by ₹ 7, 84, 670.
(i) What was the sale receipt of the company during second year?
(ii) What was the total sale receipt of the company during these two years?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 36

Question 17.
A number exceeds 8, 59, 470 by 3, 00, 999. What is the number?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 1 Number System (Consolidating the Sense of Numberness) 37

Selina Concise Mathematics Class 6 ICSE Solutions

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13C.

Other Exercises

Question 1.
Solution:
(i) Place the protractor in such a way that its centre is exactly at the vertex O of the given angle AOB and the base line lies along the arm OA. Read off the mark through which the arm OB passes, starting from 0° on the side A.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.1
We find that ∠AOB = 45°.
(ii) The given angle is ∠PQR. Place the protractor in such a way that its centre is exactly on the vertex Q of the given angle and the base line lies along the arm QR.Read off the mark through which the arm QP passes, starting from 0° on the side of R.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.2
We find that ∠PQR = 67°
(in) The given angle is ∠DEF. Place the protractor in such a way that its centre is exactly on the vertex E of the given angle and the base line lies along the arm ED. Read off the mark through which the arm EF passes, starting from 0° on the side of D.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.3
We find that ∠DEF = 130°
(iv) The given angle is ∠LMN. Place the protractor in such a way that its centre is exactly on the vertex M of the given angle and the base line lies along the arm ML. Read off the mark through which the arm MN passes, starting from 0° on the side of L.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.4
We find that ∠LMN = 50°
(v) The given angle is ∠RST. Place the protractor in such a way that its centre is exactly on the vertex S of the given angle and the base line lies along the arm SR. Read off the mark through which the arm ST passes, starting from 0° on the side of R.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.5
We find that the ∠RST = 130°.
(vi) The given angle is ∠GHI. Place the protractor in such a way that its centre is exactly on the vertex H of the given angle and the base line lies along the arm HI. Read off the mark through which the arm HG passes, starting from 0° on the side of I.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q1.6
We find that ∠GHI = 70°

Question 2.
Solution:
(i) Draw a ray OA. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OA. Starting from 0° on the side of A, look for the 25° mark on the protractor. Mark a point B at this 25° mark. Remove the protractor and draw the ray OB. Then ∠AOB is the required angle.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.1
(ii) Draw a ray OA. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OA. Starting from 0° on the side of A, look for the 72° mark on the protractor. Mark a point B at this 72° mark. Remove the protractor and draw the ray OB. Then,
∠AOB is the required angle of measure 72°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.2
(iii) Draw a ray OA. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OA. Starting from 0° on the side of A, look for the 90° mark on the protractor. Mark a point B at this 90° mark. Remove the protractor and draw the ray OB. Then ∠AOB is the required angle whose measure is 90°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.3
(iv) Draw a ray OA. Place the protractor in such a way that its centre exactly lies at O and the base line lies along OA. Starting from 0° on the side of A, look for the 117° mark on the protractor. Mark a point B at this 117° mark. Remove the protractor and draw the ray OB. Then ∠AOB is the required angle whose measure is 117°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.4
(v) Draw a ray OP. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OP. Starting from 0° on the side of P, look for the 165° mark on the protractor. Mark a point Q at this 165° mark. Remove the protractor and draw the ray OQ. Then, ∠POQ is the required angle whose measure is 165°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.5
(vi) Draw a ray OP. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OP. Starting from 0° on the side of P, look for the 23° mark on the protractor. Mark a point Q at this 23° mark. Remove the protractor and draw the ray OQ. Then ∠POQ is the required angle whose measure is 23°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.6
(vii) Draw a ray OA. Place the protractor in such a way that its centre lies exactly at O and the base line lies along OA. Starting from 0° on the side of A,Took for the 180° mark on the protractor. Mark a point B on this 180° mark. Remove the protractor and draw the ray OB. Then ∠AOB is the required angle whose measure is 180°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.7
(viii) Draw a ray Rs. Place the protractor in such away that its centre lies exactly at R and the base line lies along RS. Starting from 0° on the side of S, look for the 48° mark on the protractor. Mark a point T at this 48° mark. Remove the protractor and draw the ray RT. Then, ∠SRT is the required angle whose measure is 48°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q2.8

Question 3.
Solution:
On measuring the given angle ABC with the help of a protractor, it is 50°
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q3.1
Now, place the protractor on EF in such a way that its centre lies on E exactly and base with the line EF.
Now read off the mark through with the arm ED passes at 50°.
Join DE,
Then ∠DEF is equal to 50° i.e. equal to ∠ABC.

Question 4.
Solution:
Steps of construction :
(i) Draw a line segment AB = 6 cm.
(ii) Take a point C on AB such that AC = 4 cm.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13C Q4.1
(iii) Place protractor with its centre at C and base along CB.
(iv) Mark a point D against 90°.
(v) Remove the protractor and join DC. Then DC ⊥ AB. Ans.

Hope given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13C are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

Other Exercises

Divide :

Question 1.
x2 – 5x + 6 by x – 3
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 1

Question 2.
ax2 – ay2 by ax + ay
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 2

Question 3.
x4 – y4 by x2 – y2
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 3

Question 4.
acx2 + (bc + ad)x + bd by (ax + b)
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 4

Question 5.
(a2 + 2ab + b2)- (a2 + 2ac + c2) by 2a + b + c
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 5

Question 6.
\(\frac { 1 }{ 4 }\) x2 – \(\frac { 1 }{ 2 }\) x- 12 by \(\frac { 1 }{ 2 }\) x – 4
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 6

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5

Other Exercises

Factorize each of the following expressions :
Question 1.
16x2-25y2
Solution:
16x2 – 25y2 = (4x)2 – (5y)2    {∵ a2 – b2 = (a + b) (a – b)}
= (4x + 5y) (4x – 5y)

Question 2.
27x2 – 12y2
Solution:
27x2 – 12y2 = 3 (9x2 – 4y2)  {∵ a2 -b2 = (a + b) (a – b)}
= 3 [(3x)2 – (2y)2]
= 3 (3x + 2y) (3x – 2y)

Question 3.
144a2 – 289b2
Solution:
144a2 – 289b2 = (12a)2 – (17b)2    { ∵ a2 – b2 = (a + b) (a – b}
= (12a+ 17b) (12a- 17b)

Question 4.
12m2 – 27
Solution:
12m2 – 27 = 3 (4m2 – 9)
= 3 {(2m)2-(3)2}   {∵ a2 – b2 = (a + b) (a – b)}
= 3 (2m + 3) (2m – 3)

Question 5.
125x2 – 45y2
Solution:
125x2 – 45y2 = 5 (25x2 – 9y2)
= 5 {(5x-)2 – (3y)2}    {∵ a2 – b2 = (a + b) (a – b}
= 5 (5x + 3y) (5x – 3y)

Question 6.
144a2 – 169b2
Solution:
144a2 – 169b2 = (12a)2 – (13b)2    {∵ a2 -b2 = (a + b) (a – b)}
= (12a + 13b) (12a-13b)

Question 7.
(2a – b)2 – 16c2
Solution:
(2a – b)2 – 16c2 = (2a – b)2 – (4c)2   {∵ a2 – b2 = (a + b) (a – b)}
= (2a – b + 4c) (2a – b – 4c)

Question 8.
(x + 2y)2 – 4 (2x -y)2
Solution:
(x + 2y)2 – 4 (2x – y)2
= (x + 2y)2 – {2 (2x –y)}2
= (x + 2y)2 – (4x – 2y)2        {∵ a2– b2 = (a + b) (a – b)}
= (a + 2y + 4x – 2y) (x + 2y – 4x + 2y)
= 5x (-3x + 4y)

Question 9.
3a5 – 48a3
Solution:
3a5 – 48a3 = 3a3 (a2– 16)
= 3a3 {(a)2 – (4)2}        {∵ a2 – b2 = (a + b) (a – b)}
= 3a3 (a + 4) (a – 4)

Question 10.
a4 – 16b4
Solution:
a4 – 16b4 = (a2)2 – (4b2)2
= (a2 + 4b2) (a2 – 4b2)
= (a2 + 4b2) {(a)2 – (2b)2 }   { ∵ a2 – b2 = (a + b) (a – b)}
= (a2 + 4b2) (a + 2b) (a – 2b)

Question 11.
x8 – 1
Solution:
x8 – 1 = (x4)2 – (1)2
= (x4 + 1) (x4 – 1)
= (x4+ 1) I (x2)2 – (1)2}             {∵ a2 – b2 = (a + b) (a – b)}
= (x4 + 1) (x2 + 1) (x2 – 1)
= (x4 + 1) (x2 + 1) {(x)2 – (1)2}
= (x4+ 1)(x2 + 1)(x+ 1)(x- 1)
= (x-1)(x+ 1) (x2 + 1) (x4 + 1)

Question 12.
64 – (a + 1)2
Solution:
64 – (a + 1)2 = (8)2 – (a + 1)2    {∵ a2 – b2 = (a + b) (a – b)}
= (8 + a + 1) (8 – a – 1)
= (9 + a) (7 – a)

Question 13.
36l2 – (m + n)2
Solution:
36l2 – (m + n)2 = (6l)2 – (m + n)2        {∵  a2 – b2 = (a + b) (a – b)}
= (6l + m + n) (6l – m – n)

Question 14.
25x4y4 – 1
Solution:
25x4y4 – 1 = (5x4y4)2 – (1)2         { ∵  a2 – b2 = (a + b) (a – b)}
= (5x4y4  + 1) (5x2y2  – 1)

Question 15.
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 1.1
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 1
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 2

Question 16.
x3 – 144x
Solution:
x3 – 144x = x (x2 – 144)
= x {(x)2 – (12)2}       {∵ a2 – b2 = (a + b) (a – b)}
=  x (x + 12) (x – 12)

Question 17.
(x – 4y)2 – 625
Solution:
(x – 4y)2 – 625
= (x – 4y)2 – (25)2     {∵ a2 – b2 = (a + b) (a – b)}
= (x – 4y + 25) (x -4y – 25)

Question 18.
9 (a – b)2 – 100 (x -y)2
Solution:
9(a-b)2– 100(x-y)2
= {3(a-b)}2-{10(x-y)}2      {∵ a2 – b2 = (a + b) (a – b)}
= (3a – 3b)2 – (10x – 10y)2
= (3a – 3b + 10x – 10y) (3a – 3b – 10x + 10y)

Question 19.
(3 + 2a)2 – 25a2
Solution:
(3 + 2a)2 – 25a2
= (3 + 2a)2 – (5a)2      (∵ a2 – b2 = (a + b) (a – b)}
= (3 + 2a + 5a) (3 + 2a – 5a)
= (3 + 7a) (3 – 3a)
= (3 + 7a) 3 (1 – a)
= 3(1-a) (3 +7a)

Question 20.
(x + y)2 – (a – b)2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 3

Question 21.
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 4
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 5

Question 22.
75a3b2 – 108ab4
Solution:
75a3b2 – 108ab4
= 3ab2 (25a2 – 36b2)
= 3ab2 {(5a)2 – (6b)2}         {∵ a2 – b2 = (a + b) (a – b)}
= 3ab2 (5a + 6b) (5a – 6b)

Question 23.
x5– 16x3
Solution:
x5 – 16x3 = x3 (x2 – 16)
= x3 {(x)2 – (4)2} {∵ a2 – b2 = (a + b) (a – b)}
= x3 (x + 4) (x – 4)

Question 24.
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 6
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 7

Question 25.
256x5 – 81x
Solution:
256x5– 81x = x(256x4– 81)
= x {(16x2)2 – (9)2}      {∵ a2 – b2 = {a + b) (a – b)}
= x (16x2 + 9) (16x2 – 9)
= x (16x2 + 9) {(4x)2 – (3)2}
= x (16x2 + 9) (4x + 3) (4x-3)

Question 26.
a4 – (2b + c)4
Solution:
a4 – (2b + c)4
= (a2)2 – [(2b + c)2]2    {∵ a2 – b2 = (a + b) (a – b)}
= {a2 + (2b + c)2} {a2 – (2b + c)2}
= {a2 + (2b + c)2} {(a)2 – (2b + c)2}
= {a2 + (2b + c)2} (a + 2b + c) (a -2b- c)

Question 27.
(3x + 4y)4 – x4
Solution:
(3x + 4y)4 – x4 – [(3x + 4y)2]2 – (x2)2
= [(3x + 4y)2 + x2] [(3x + 4y)2 – x2]       {∵  a2 – b2 = (a + b) (a – b)
= [(3x + 4y)2 + x2] [(3x + 4y + x) (3x + 4y – x)]
=   [(3x + 4y)2 + x2] (4x + 4y) (2x + 4y)
= [(3x + 4y)2 + x2] 4 (x + y) 2 (x + 2y)
= 8 (x + y) (x + 2y) [(3x + 4y)2 + x2]

Question 28.
p2q2 – p4q4
Solution:
p2q2– p4q4 =p2q2 (1 -p2q2)
=p2q2 [(1)2 – (pq)2]   {∵ a2 – b2 = (a + b) (a – b)
= p2q2 (1 +pq) (1 -pq)

Question 29.
3x3y – 243xy3
Solution:
3x3y – 243xy3
= 3xy (x2 – 81y2)
= 3xy [(x)2 – (9y)2]
= 3xy (x + 9y) (x – 9y)

Question 30.
a4b4 – 16c4
Solution:
a4b4 – 16c4 = (a2b2)2 – (4c2)2
= (a2b2 + 4c2) (a2b2 – 4c2)
= (a2b2 + 4c2) [(ab)2 – (2c)2]      {∵ a2 – b2 = (a + b) (a – b)
= (a2b2 + 4c2) (ab + 2c) (ab – 2c)

Question 31.
x4-625
Solution:
x4 – 625 = (x2)2 – (25)2   {∵ a2 – b2 – (a + b) (a – b)
= (x2 + 25) (x2 – 25)
= (x2 + 25) [(x)2 – (5)2]
= (x2 + 25) (x + 5) (x – 5)

Question 32.
x4-1
Solution:
x4 – 1 = (x2)2 – (1)2 = (x2 + 1) (x2 – 1)
= (x2 + 1) [(x)2 – (1)2]
= (x2 + 1) (x + 1) (x – 1)

Question 33.
49 (a – b)2 -25 (a + b)2
Solution:
49 (a – by -25 (a + b)2
= [7 (a – b)]2 – [5 (a + b)]2
= (7a – 7b)2 – (5a + 5b)2  {∵ a2 – b2 = (a + b) (a – b)
= (7a -7b + 5a + 5b) (7a – 7b -5a- 5b)
=(12a – 2b)(2a – 12b)
= 2 (6a – b) 2 (a – 6b)
= 4 (6 a- b) (a – 6b)

Question 34.
x – y – x2 + y2 
Solution:
x-y-x2 + y2 = (x-y)-(x2-y2) {∵ a2 – b2 = (a + b) (a – b)
= {x-y)-(x + y)(x-y)
= (x-y)(1 – x – y)

Question 35.
16 (2x – 1)2 – 25y2
Solution:
16 (2x – 1)2 – 25y2
= [4 (2x – 1)]2 – (5y)2
= (8x – 4)2 – (5y)2
= (8x – 4 + 5y) (8x -4-5y)
= (8x + 5y – 4) (8x – 5y – 4)

Question 36.
4 (xy + 1)2 – 9 (x – 1)2
Solution:
4 (xy + 1)2 – 9 (x – 1)2
= [2 (xy + 1)]2 – [3 (x – 1)]2
= (2xy + 2)2 – (3x – 3)2 {∵ a2 – b2 = (a + b) (a – b)
= (2xy + 2 + 3x – 3) (2xy + 2 – 3x + 3)
= (2xy + 3x – 1) (2xy – 3x + 5)

Question 37.
(2x + 1)2 – 9x4
Solution:
(2x + 1)2 – 9x4 = (2x + 1)2 – (3x2)2    {∵ a2 – b2 = (a + b) (a – b)
= (2x + 1 + 3x2) (2x + 1 – 3x2)
= (3x2 + 2x + 1) (-3x + 2x + 1)

Question 38.
x4 – (2y- 3z)2
Solution:
x4 – (2y – 3z)2 = (x2)2 – (2y – 3z)2
= (x2 + 2y- 3z) (x2 – 2y + 3z)

Question 39.
a2-b2 +a-b
Solution:
a2 – b2 + a – b
= (a + b) {a – b) + 1 (a – b)
= (a – b) (a + b + 1)

Question 40.
16a4 – b4
Solution:
16a4 – b4
= (4a2)2 – (b2)2            { ∵  a2 – b2 = (a + b) (a – b)
= (4a2 + b2) (4a2 – b2)
= (4a2 + b2) {(2a)2 – (b)2}
= (4a2 + b2) (2a + b) (2a – b)

Question 41.
a4 – 16 (b – c)4
Solution:
a4 – 16 (b- c)4 = (a2)2 – [4 (b – c)2]2 { ∵  a2 – b2 = (a + b) (a – b)
= [a2 + 4 (b – c)2] [a2 – 4 (b – c)2]
= [a2 + 4 (b – c)2] [(a)2 – [2 (b – c)]2]
= [a2 + 4 (b – c)2] [(a)2 – (2b – 2c)2]
= [a2 + 4 (b – c)2] (a + 2b – 2c) (a – 2b + 2c)

Question 42.
2a5 – 32a
Solution:
2a5 – 32a = 2a (a4 – 16)
= 2a [(a2)2 – (4)2]  {∵  a2 – b2 = (a + b) (a – b)
= 2a (a2 + 4) (a2 – 4)]
= 2a (a2 + 4) [(a)2 – (2)2]
= 2a (a2 + 4) (a + 2) (a – 2)

Question 43.
a4b4 – 81c4
Solution:
a4b4 – 81c4 = (a2b2)2 – (9c2)2
= (a2b2 + 9c2) (a2b2 – 9c2) {∵ a2 – b2 = (a + b) (a – b)
= (a2b2 + 9c2) {(ab)2 – (3c)2}
= (a2b2 + 9c2) (ab + 3c) (ab – 3c)

Question 44.
xy9-yx9
Solution:
xy9 – yx9 = xy (y8 – x8)
= xy [(y4)2 – (x4)2] {∵  a2 – b2 = (a + b) (a – b)}
= xy(y4 + x4)(y4-x4)
= xy (y4 + x4) {(y2)2 – (x2)2}
= xy (y4 + x4) (y2 + x2) (y2 – x2)
= xy (y4 + x4) (y2 + x2) (y + x) (y – x)

Question 45.
x3 -x
Solution:
x3-x = x(x2– 1)
= x [(x)2 – (1)2] = x (x + 1) (x – 1)

Question 46.
18a2x2 – 32
Solution:
18a2x2 – 32
= 2 [9a2x2 – 16]
= 2 [(3ax)2 – (4)2]   {∵ a2 – b2 = (a + b) (a – b)
= 2 (3ax + 4) (3ax – 4)

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B

RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B

These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13B.

Other Exercises

Question 1.
Solution:
(i) Obtuse angle
(ii) Right angle
(iii) straight angle
(iv) Reflex angle
(v) Acute angle
(vi) Complete angle

Question 2.
Solution:
We know that an acute angle is less than 90°
(ii) a right angle is equal to 90°
(iii) an obtuse angle is greater than 90° but less than 180°
(iv) an angle equal to 180° is a straight angle
(v) angle greater than 180° but less than 360° is called a reflex angle
(vi) angle equal to 360° is called a complete angle and angle equal to 0° is called a zero angle. Now the angles are :
(i) acute
(ii) obtuse
(iii) obtuse
(iv) right
(v) reflex
(vi) complete
(vii) obtuse
(viii) obtuse
(ix) acute
(x) acute
(xi) zero
(xii) acute Ans.

Question 3.
Solution:
(i) One right angle = 90°
(ii) Two right angles = (2 x 90)° = 180°
(iii) Three right angles = (3 x 90)° = 270°
(iv) Four right angles = (4 x 90)° = 360°
(v) \(\frac { 2 }{ 3 } \) right angle = \(\left( \frac { 2 }{ 3 } \times { 90 }^{ O } \right) \) = 60°
(vi) 1½ right angle = \(\left( 1\frac { 1 }{ 2 } \times { 90 }^{ O } \right) \)
\(\left( \frac { 3 }{ 2 } \times { 90 }^{ O } \right) \) = 135°

Question 4.
Solution:
(i) When it is 3 o’ clock, the minute hand is at 12, and hour hand is at 3 as shown in the figure, clearly, the angle between the two hands 90°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q4.1
(ii) When it is 6 o’ clock, the minute hand is at 12 and the hour hand is at 6 as shown in the figure. Clearly, the angle between the two hands of the clock is a straight angle is i.e. 180°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q4.2
(iii) When it is 12 o’ clock, both the hands of the clock lie at 12 as shown in the figure. Clearly, the angle between the two hands = 0°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q4.3
(iv) When it is 9 o’ clock, the minute hand is at 12 and the hour hand is at 9 as shown in the figure. Clearly, the angle between the two hands = 90°.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q4.4

Question 5.
Solution:
(i) Take the rular and draw any ray OA. Again using the rular, starting from O, draw a ray OB in such a way that the angle formed is less than 90°. Then, ∠AOB is the required acute angle.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q5.1
(ii) Take the rular and draw any ray OA. Now, starting from O, draw another ray OB, with the help of the rular, such that the angle formed is greater than a right angle.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q5.2
Then, ∠AOB is the required obtuse angle.
(iii) Take a rular and draw any ray OA. Now, starting from O, draw ray OB in the opposite direction of the ray OA. Then ∠AOB is the required straight angle.
RS Aggarwal Class 6 Solutions Chapter 13 Angles and Their Measurement Ex 13B Q5.3

Hope given RS Aggarwal Solutions Class 6 Chapter 13 Angles and Their Measurement Ex 13B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

The Patriot Summary by Robert Browning

We have decided to create the most comprehensive English Summary that will help students with learning and understanding.

The Patriot Poem Summary by Robert Browning

The Patriot Summary by Robert Browning About the Poet

Robert Browning (1812-1889) was one of the most outstanding poetic geniuses from the Victorian Era, the most prolific of all ages in the literary history of England. As a poet, his oeuvre primarily rests on his unique style of expression and mastery over the use of language to deal with an array of unusual subjects, and the immaculate ability to combine the elements of drama with poetry. His sense of psychology precedes Freud, and his refusal to commit to any prevailing worldview marks him as a precursor to modernist thought.

Though he accomplished himself as a writer, scholar and musician early in life, he developed a true passion for poetry when he was introduced to the work of P.B. Shelley. From Shelley, Browning developed the Romantic ideal, which sought to find transcendence through exploration of the individual’s sensibility. Browning’s early life and work was largely defined by this sensibility.

His first published work, Pauline, was a remarkable success in 1833. But his subsequent publication, a long and complex poem titled Sordello, was a failure. Critics of his time labelled him difficult and obscure. Between 1841 and 1846, in a series of pamphlets under the general title of Bells and Pomegranates, he published seven plays in verse, including Pippa Passes, A Blot in the ’Scutcheon, and Luria.

However, he was beginning to establish the dramatic monologue form that would ensure his legacy. This form uses a narrator, usually of dubious morality, who addresses someone in a high-stakes situation. His most famous works were written in this form, including- Porphyria’s Lover and My Last Duchess. These works helped cement his interest in psychological complexity and the human tendency to constantly shift perspectives and opinions.

In 1845, he fell in love with poet Elizabeth Barrett. Subsequently, they eloped in order to marry. They lived a happy life together, mostly in Italy. In 1855, Browning published a collection called Men and Women, containing most of his best known poems. After Elizabeth died in 1861, Browning moved back to London, where he would finally achieve the success that had long eluded him.

He published other collections like Dramatis Personae, but it was his long work The Ring and the Book that finally made him famous. His subsequent poetry continued to expand his fame in later years. At the time Browning died in 1889, he was perhaps the most famous poet in England next to William Wordsworth.

The Patriot Summary About The Poem

‘The Patriot’ is one of the best-known poems by the 19th century English poet Robert Browning. It is one of those pieces for which Browning adopted a new poetic device called ‘dramatic monologue’. As such, the poem revolves around the narrator who is talking to himself in a ‘dramatic’ way. His monologue reveals the story of a man who was once idolised by people as a great hero, but was subsequently misunderstood and rejected by the latter.

Today, he is going to be executed in front of the public, for a crime which he says he has not committed. The tragic tone of his monologue ends on a positive note, when he expresses hope that when he reaches heaven after his death, God will save him from the public’s misunderstood views.

Another striking feature of this poem lies in its deep political underpinnings suggesting a situation that resembles the fall of many leaders, who are adored by public in the beginning but misunderstood and eventually disgraced due to the fickleness of public opinion. In all, the sensitive and empathetic treatment of the narrator’s situation; and the poet’s brilliance as a master of poetic craft make this poem a remarkable one.

The Patriot Summary of the poem

‘The Patriot’ is a dramatic verse that deals with the fickleness of public opinion and hero-worship. The speaker of the poem is a patriot. He thinks of his glorio.us past. A year ago he was given a grand welcome on his arrival to the town. People had thrown roses and myrtle in his path. The church-spires were decorated with bright flags. The house-roofs were full of people who wanted to have a look at him. Bells rang to announce the patriot’s arrival. The frenzy and madness exceeded all limits. People were even ready to catch the sun for him.

The Patriot Poem Summary
The Patriot Poem Summary

But everything has changed now. The patriot is being taken to the scaffold for all his ‘misdeeds’. There is nobody on the house-tops now. Everyone knows that today, the best of the sights is at the foot of the scaffold. He is going in the rain with his wrists tied behind. People are throwing stones at him and his forehead is bleeding. What an ill-fate to a man who spent all his life for his countrymen!

Even in the midst of tragedy, the poem ends quite optimistically. Death is not the end of everything. The patriot hopes that since he did not receive his reward in this world, he will be rewarded in the other world. He feels safe in the hands of God. Thus the poem also becomes an expression of Browning’s optimistic philosophy of life. “God is in His heaven and all is well with the world.”

The Patriot Summary Critical Analysis

“The Patriot” is a poem comprising 6 stanzas. Each stanza consists of 5 lines and its rhyming pattern is ababa. It is a dramatic monologue. Dramatic monologue is a literary device in which a character freely gives vent to his feelings in front of the audience in order to reveal the inner working of his mind.

As such, the hero of this interesting but tragic poem talks to the audience aloud and tells us that how he was acclaimed at one stage and put to a tragic end at another. Symbolically, the poem has unmistakable political overtones as the major theme of it seems to be the rise and fall of leaders in the contemporary politics.

The first stanza is an elaborate description of how the poet is welcomed back with pomp and ceremony by all the townspeople. His path is laden with roses and myrtles, which signify love, respect and honour being showered on the patriot by the residents of the town who have clambered onto their roofs to get a glimpse of the patriot and welcome him home and showcase their gratuity.

This creates an imagery of the house itself moving and swaying with the weight and number of people. Even the church spires were decorated with fiery coloured flags. This gives the reader an idea of the enormity of the celebrations. In the last line the poet discloses to the reader that these events occurred on this date, exactly a year ago.

In the second stanza, the narrator says how the ringing of the church bells infected the air and it seemed to be echoing the celebratory noise. The walls of the city, which were already on the verge of erosion, due to time, reflected the impact of the din created by the crowd. It seemed to conduct tremors. The patriot here is telling the people that how he doesn’t want all the cheers and applause, but wants the people to fetch the sun from the skies for him. He wants the power, glory, admiration and honour. He wants to live in their memories as an immortal hero.

Here a side of the patriot is shown that searches, not, for momentary praise, but for everlasting recognition and glory. He doesn’t want extravagant celebrations that can die down with time. He is looking for something more permanent. For a while therefore, he imagines asking people to fetch him the sun, a symbol of immortality, power, honour and glory. The presumed answer of the crowd is reflective of their frivolous nature.

They would immediately ask the patriot what more did he require. This indicates that though people who had assembled to welcome him were zealous and passionate, they lacked a high degree of sensibility. The way they are expected to react to their hero’s demand only suggests their uncritical inclination towards hero worship.

The third stanza acts as a conjunction for the transition from the past to . the present. The patriot says that despite him asking the townspeople to get him the sun, in the end it was he who leaped for it and got it for the people, who he refers to as his beloved friends. This act that he does is such in nature that had he left it undone, no other man could have accomplished it. This stanza has a tone of regret.

This can be deciphered by the use of “Alack!” or Alas. Also, the last two lines indicate towards this as the patriot mourns about how his deed has been repaid by the people. His “harvest” is what he has reaped, whereas what he had sown was bringing glory, power and honour to the people. The first two stanzas narrate the incidents of a year back, when the patriot was given celebrity status. This stanza acts as a synopsis to the current events.

In the fourth stanza, the speaker says that there are no more people on the roof tops, trying to catch a glimpse of the patriot. Only a few cripples can be seen at the windows. The patriot takes up a sarcastic tone at this point and says that this is because the best sight is at the gate of the gallows. In this stanza, a contrast is drawn between the time when the roof tops were heaving with people, celebrating the patriot’s deeds, and the current scenario where the people are assembled, but near the gallows.

Only the ones who cannot travel to the spot of execution, the ones who are crippled, are staring outside their windows to get a look at the patriot. The patriot’s anguish is seen when he taunts about the townspeople, saying they will be found, not on the roofs, but on the site of the execution, or better still, at the foot of the gallows. This stanza is suggestive of the patriot’s fate that he is being taken to be executed.

In the fifth stanza, the poet has employed the sad imagery of the patriot walking in the rain, heading towards the gallows. His wrists are tied tightly behind his back with a rope that cuts through his skin. He can feel blood trickling down his forehead, but he cannot know for sure as his hands are bound, so he can’t touch and feel. His cuts are because of the stones being flung at him by anybody and everybody. The picture being projected in this stanza is a very pitiable one as it is in direct contrast with the imagery of the first and the second stanza.

The patriot provides an ambiguous explanation for this transition, saying he is being punished for the misdeeds that he has committed within this one year. Despite the fact that no rigid and stable details have been given of the patriot’s act, it can be inferred that most probably he has indulged in acts of treachery, betrayal or any such unpatriotic act. This conclusion can be reached keeping the title of the poem in mind. The main gist of this stanza is the description of the poet’s walk of shame.

The sixth and concluding stanza of the poem begins with the patriot declaring how he is leaving, the same way that he entered. He is walking towards his death through the same streets on which he had entered the town and was welcomed as a celebrity, a hero. Even the most important, the most loved people have lost their glamour and glory. The most triumphant have also fallen. The patriot’s religious beliefs have been reflected and his belief in afterlife has been showcased when he mentions how he will be received by God. If God might ask him, now that he has been paid for his deeds by the world, what more does he owe to God. The patriot’s reply to this has shades of faith and optimism. He replies saying that his real repayment will be done by God.

He is placing his trust in God as he knows that he has committed no moral wrongs and the almighty is always just and fair. Hence, he is safe with God as he won’t have to face anymore undeserving punishments and will be truly and justly rewarded for his acts or deeds. In all, the poem is a superb example of current political upheaval and changed public opinion. The writer wants to suggest that nothing remains the same in the world politics. It is a world of self-interest and selfish people who, for individual benefits, may go against the common good of the country.

The Patriot Summary Word-Meanings

  1. myrtle – a decorative flower
  2. heave – drag, pull
  3. sway – swing, bend
  4. spires – church towers
  5. repel – keep away
  6. yonder – at some distance in the direction indicated; over there
  7. alack – expression of regret
  8. leaped – jumped
  9. nought – nothing
  10. palsied – paralysed
  11. trow – think, believe
  12. fling – throw or hurl something
  13. owe – have an obligation to pay or repay.

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method

Unitary Method Exercise 13A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The price of 25 identical articles is ₹ 1,750. Find the price of :
(i) one article
(ii) 13 articles
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 1

Question 2.
A motorbike travels 330 km in 5 litres of petrol. How much distance will it cover in :
(i) one litre of petrol?
(ii) 2.5 litres of petrol?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 2

Question 3.
If the cost of a dozen soaps is ₹ 460.80, what will the cost of:
(i) each soap?
(ii) 15 soaps?
(iii) 3 dozen soaps?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 3

Question 4.
The cost of 35 envelops is ₹ 105. How many envelops can be bought for ₹ 90?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 4

Question 5.
If the cost of 8 cans of juice is ₹ 280, then what will be the cost of 6 cans of juice?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 5

Question 6.
For ₹ 378, 9 cans of juice can be bought, then how many cans of juice can be bought for ₹ 504?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 6

Question 7.
A motorbike travels 425 km in 5 hours. How much distance will be covered by it in 3.2 hours?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 7

Question 8.
If the cost of a dozen identical articles is ₹ 672, what will be the cost of 18 such articles?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 8

Question 9.
A car covers a distance of 180 km in 5 hours.
(i) How much distance will the car cover in 3 hours with the same speed ?
(ii) How much time will the car take to cover 54 km with the same speed?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 9

Question 10.
If it has rained 276 cm in the last 3 days, how many cm of rain will fall in one week (7 days) ?
Assume that the rain continues to fall at the same rate.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 10

Question 11.
Cost of 10 kg of wheat is ₹ 180.
(i) What is the cost of 18 kg of wheat?
(ii) What quantity of wheat can be purchased in ₹ 432?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 11

Question 12.
Rohit buys 10 pens for ₹ 150 and Manoj buys 14 pens for ₹ 168. Who got the pens cheaper?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 12

Question 13.
A tree 24 m high casts a shadow of 15 m. At the same time, the length of the shadow casted by some other tree is 6 m. Find the height of the tree.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 13

Question 14.
A loaded truck travels 18 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 14

Unitary Method Exercise 13B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Weight of 15 books is 6 kg. What is the weight of 45 such books?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 15

Question 2.
A made 84 runs in 6 overs and B made 126 runs in 7 overs. Who made more runs per over?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 16

Question 3.
Geeta types 108 words in 6 minutes. How many words would she type in half an hour?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 17

Question 4.
The temperature dropped 18 degree Celsius in the last 24 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next 18 days?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 18

Question 5.
Mr. Chopra pays ₹ 12,000 as rent for 3 months. How much does he has to pay for a year if the rent per month remains same?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 19

Question 6.
A truck requires 108 litres of diesel for covering a distance of 1188 km. How much diesel will be required by the truck to cover a distance of 3300 km?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 20

Question 7.
If a deposit of ₹ 2,000 earns an interest of ₹ 500 in 3 years, how much interest would a deposit of ₹ 36,000 earn in 3 years with the same rate of simple interest?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 21

Question 8.
If John walks 250 steps to cover a distance of 200 metres, find the distance covered by him in 350 steps.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 22

Question 9.
25 metres of cloth costs ₹ 1,012.50.
(i) What will be the cost of 20 metres of cloth of the same type?
(ii) How many metres of the same kind can be bought for ₹ 1,620?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 23

Question 10.
In a particular week, a man works for 48 hours and earns ₹ 4,320. But in the next week he worked 6 hours less, how much has he earned in this week?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 13 Unitary Method 24

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

Proportion Exercise 12A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In each of the following, check whether or not the given ratios form a proportion :
(i) 8 : 16 and 12 : 15
(ii) 16 : 28 and 24 : 42
(iii) 12 ÷ 3 and 8 ÷ 2
(iv) 25 : 40 and 20 : 32
(v) \(\frac { 15 }{ 18 }  and \frac { 10 }{ 12 }\)
(vi) \(\frac { 7 }{ 8 }\) and 14 : 16
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 1
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 2

Question 2.
Find the value of x in .each of the following proportions :
(i) x : 4 = 6 : 8
(ii) 14 : x = 7 : 9
(iii) 4 : 6 = x : 18
(iv) 8 : 10 = x : 25
(v) 5 : 15 = 4 : x
(vi) 16 : 24 = 6 : x
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 3

Question 3.
Find the value of x so that the given four numbers are in proportion :
(i) x, 6, 10 and 15
(ii) x, 4, 15 and 30
(iii) 2, x, 10 and 25
(iv) 4, x, 6 and 18
(v) 9, 12, x and 8
(vi) 4, 10, 36 and x
(vii) 7, 21, x and 45
(viii) 6, 8, 12 and x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 4

Question 4.
The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 5

Question 5.
Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 6

Question 6.
Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 7

Question 7.
The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 8

Question 8.
The ratio of the sale of eggs on a Sunday and that of the whole week at a grocery shop was 2 : 9. If the total value of the sale of eggs in the same week was Rs 360, find the value of the sale of eggs that Sunday.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 9

Question 9.
The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg ; find the weight of copper in the alloy.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 10

Question 10.
The ratio of the number of girls to the number of boys in a school is 2 : 5. If the number of boys is 225 ; find:
(i) the number of girls in the school.
(ii) the number of students in the school.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 11

Question 11.
In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 12

Question 12.
Make set of all possible proportions from the numbers 15, 18, 35 and 42.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 13

Proportion Exercise 12B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If x, y and z are in continued proportion, then which of the following is true :
(i) x : y = x : z
(ii) x : x = z : y
(iii) x : y = y : z
(iv) y : x = y : z
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 14

Question 2.
Which of the following numbers are in continued proportion :
(i) 3, 6 and 15
(ii) 15, 45 and 48
(iii) 6, 12 and 24
(iv) 12, 18 and 27
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 15

Question 3.
Find the mean proportion between
(i) 3 and 27
(ii) 0.06 and 0.96
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 16

Question 4.
Find the third proportional to :
(i) 36, 18
(ii) 5.25, 7
(iii) ₹ 1.60, ₹ 0.40
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 17
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 18

Question 5.
The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 19

Question 6.
If (4x + 3y) : (3x + 5y) = 6 : 7, find :
(i) x : y
(ii) x, if y = 10
(iii) y, if x = 27
Solution:
</spanSelina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 20
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 21

Question 7.
If \(\frac { 2y+5x }{ 3y-5x } =2\frac { 1 }{ 2 }\), find:
(i) x : y
(ii) x, if y = 70
(iii) y, if x = 33
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 22
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 23

Proportion Exercise 12C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Are the following numbers in proportion:
(i) 32, 40, 48 and 60 ?
(ii) 12,15,18 and 20 ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 24

Question 2.
Find the value of x in each of the following such that the given numbers are in proportion.
(i) 14, 42, x and 75
(ii) 45, 135, 90 and x
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 25

Question 3.
The costs of two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800 ; find the cost of the second article.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 26

Question 4.
The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 27

Question 5.
The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 28

Question 6.
A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 29

Question 7.
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 30

Question 8.
Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 31

Question 9.
10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 32

Question 10.
The length of two ropes are in the ratio 7 : 5. Find the length of:
(i) shorter rope, if the longer one is 22.5 ni
(ii) longer rope, if the shorter is 9.8 m.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 33

Question 11.
If 4, x and 9 are in continued proportion, find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 34

Question 12.
If 25, 35 and x are in continued proportion, find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion 35

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio

Ratio Exercise 11A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following ratios in its simplest form :
(a) (i) 4 : 6
(ii) 48 : 54
(iii) 200 : 250
(b) (i) 5 kg : 800 gm
(ii) 30 cm : 2 m
(iii) 3 m : 90 cm
(iv) 2 years : 9 months
(v) 1 hour : 45 minutes
(vi) 4 min : 45 sec
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 43
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 1
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 2
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 3

Question 2.
A field is 80 m long and 60 m wide. Find the ratio of its width to its length.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 4

Question 3.
State, true or false :
(i) A ratio equivalent to 7 : 9 is 27 : 21.
(ii) A ratio equivalent to 5 : 4 is 240 : 192.
(iii) A ratio of 250 gm and 3 kg is 1 : 12.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 5

Question 4.
Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 6

Question 5.
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 7

Question 6.
Find the ratio between 3.5 m, 475 cm and 2.8 m.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 8

Question 7.
Find the ratio between 5 dozen and 2 scores. [1 score = 20]
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 9

Ratio Exercise 11B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The monthly salary of a person is Rs. 12,000 and his monthly expenditure is Rs 8,500. Find the ratio of his:
(i) salary to expenditure
(ii) expenditure to savings
(iii) savings to salary
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 10

Question 2.
The strength of a class is 65, including 30 girls. Find the ratio of the number of:
(i) girls to boys
(ii) boys to the whole class
(iii) the whole class to girls.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 11

Question 3.
The weekly expenses of a boy have increased from ₹ 1,500 to ₹ 2,250. Find the ratio of:
(i) increase in expenses to original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increase in expenses.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 12

Question 4.
Reduce each of the following ratios to their lowest terms :
(i) 1 hour 20 min : 2 hours
(ii) 4 weeks : 49 days
(iii) 3 years 4 months : 5 years 5 months.
(iv) 2 m 40 cm : 1 m 44 cm
(v) 5 kg 500 gm : 2 kg 750 gm
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 13
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 14

Question 5.
Two numbers are in the ratio 9 : 2. If the smaller number is 320, find the larger number.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 15

Question 6.
A bus travels 180 km in 3 hours and a train travels 450 km in 5 hours. Find the ratio of speed of train to speed of bus.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 16

Question 7.
In winters, a school opens at 10 a.m. and closes at 3.30 p.m. If the lunch interval is of 30 minutes, find the ratio of lunch interval to total lime of the class periods.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 17

Question 8.
Rohit goes to school by car at 60 km per hour and Manoj goes to school by scooty at 40 km per hour. If they both live in the same locality, find the ratio between the time taken by Rohit and Manoj to reach school.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 18

Question 9.
In a club having 360 members, 40 play carrom, 96 play table tennis, 144 play badminton and remaining members play volley-ball. If no member plays two or more games, find the ratio of members who play :
(i) carrom to the number of those who play badminton.
(ii) badminton to the number of those who play table-tennis.
(iii) table-tennis to the number of those who play volley-ball.
(iv) volleyball to the n umber of those who play other games.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 19

Question 10.
The length of a pencil is 18 cm and its radius is 4 cm. Find the ratio of its length to its diameter.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 20

Question 11.
Ratio of distance of the school from A’s home to the distance of the school from B’s home is 2 : 1.
(i) Who lives nearer to the school?
(ii) Complete the following table :
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 21

Question 12.
The student-teacher ratio in a school is 45 : 2. If there are 4050 students in the school, how many teachers must be there?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 22

Ratio Exercise 11C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
₹ 120 is to be divided between Hari and Gopi in the ratio 5 : 3. How much does each get?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 23

Question 2.
Divide 72 in the ratio \(2\frac { 1 }{ 2 } :1\frac { 1 }{ 2 }\)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 24

Question 3.
Divide 81 into three parts in the ratio 2 : 3 : 4.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 25

Question 4.
Divide Rs 10,400 among A, B and C in the ratio \(\frac { 1 }{ 2 } :\frac { 1 }{ 3 } :\frac { 1 }{ 4 } \)
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 26

Question 5.
A profit of Rs 2,500 is to be shared among three persons in the ratio 6 : 9 : 10. How much does each person get?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 27

Question 6.
The angles of a triangle are in the ratio 3 : 7 : 8. Find the greatest and the smallest angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 28

Question 7.
The sides of a triangle are in the ratio 3 : 2 : 4. If the perimeter of the triangle is 27 cm, find the length of each side.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 29

Question 8.
An alloy of zinc and copper weighs 12\(\frac { 1 }{ 2 }\) kg. if in the alloy, the ratio of zinc and copper is 1 : 4, find the weight of copper in it.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 30

Question 9.
How will Rs 31500 be shared between A, B and C ; if A gets the double of what B gets, and B gets the double of what C gets?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 31

Question 10.
Mr. Gupta divides Rs 81000 among his three children Ashok, Mohit and Geeta in such a way that Ashok gets four times what Mohit gets and Mohit gets 2.5 times what Geeta gets. Find the share of each of them.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 32

Ratio Exercise 11D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Which ratio is greater:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 44
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 33

Question 2.
Which ratio is smaller :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 45
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 34

Question 3.
Increase 95 in the ratio 5 : 8.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 35

Question 4.
Decrease 275 in the ratio 11 : 7.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 36

Question 5.
Decrease 850 in the ratio 17 : 6 and then increase the result in the ratio 5 : 9.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 37

Question 6.
Decrease 850 in the ratio 17 : 6 and then decrease the resulting number again in 4 : 3.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 38

Question 7.
Increase 1200 in the ratio 2 : 3 and then decrease the resulting number in the ratio 10 : 3.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 39

Question 8.
Increase 1200 in the ratio 3 : 7 and then increase the resulting number again in the ratio 4 : 7.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 40

Question 9.
The number 650 is decreased to 500 in the ratio a : b, find the ratio a : b.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 41

Question 10.
The number 800 is increased to 960 in the ratio a : b, find the ratio a : b.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 11 Ratio 42

Selina Concise Mathematics Class 6 ICSE Solutions