Online Education NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3

In Online Education NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 8
Chapter Name Comparing Quantities
Exercise Ex 8.3
Number of Questions Solved 12
Category NCERT Solutions

Online Education NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3

Question 1.
Calculate the amount and compound interest on
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 1
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 1 2
Solution.
(a) By using year by year calculation
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 2
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 3

(b) By using year by year calculation
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 4
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 5
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 6
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 7

(c) By using half year by half year calculation
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 8
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 9

(d) By using half-year by half-year calculation
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 10
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 11
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 12

NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 13
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 14
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 38

Question 2.
Kamala borrowed ₹ 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
(Hint: Find A for 2 years if interest is compounded yearly and then find SI on the 2nd year amount for \(\frac { 4 }{ 12 } \) year)
Solution.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 15

Question 3.
Fabina borrows ₹ 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much ?
Solution.
For Fabina
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 16

Question 4.
I borrowed ₹ 12,000from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what excess amount would I have to pay?
Solution.
At simple interest
P = ₹ 12000
R = 6% per annum
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 17

Question 5.
Vasudevan invested ₹ 60,000 on interest at the rate of 12% per annum compounded half yearly. What amount would he get
(i) after 6 months?
(ii) after 1 year?
Solution.
(i) after 6 months
P = ₹ 60,000
R = 12% per annum
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 18

(ii) after 1 year
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 19

Question 6.
Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after \(1\frac { 1 }{ 2 } \) years if the interest is
(i) compounded annually
(ii) compounded half yearly
Solution.
(i) compounded annually
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 20

(ii) compounded half yearly
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 21
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 22

Question 7.
Maria invested ₹ 8,000 in business. She would be paid interest at the rate of 5% per annum compounded annually. Find
(i) the amount credited against her name at the end of the second year.
(ii) the interest for the 3rd year.
Solution.
(i)
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 23

(ii)
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 24
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 25
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 26

Question 8.
Find the amount and the compound interest on ₹ 10,000 for \(1\frac { 1 }{ 2 } \) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Solution.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 27
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 28
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 29

Question 9.
Find the amount which Ram will get on ₹ 4,096 if he gave it for 18 months at \(12\frac { 1 }{ 2 } % \) per annum, interest being compounded half yearly.
Solution.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 30
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 31

Question 10.
The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.
(i) find the population in 2001.
(ii) what would he its population in 2005?
Solution.
(i)
Let the population in 2001 be P.
R = 5% p.a.
n = 2 years
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 32

(ii)
initial population in 2003
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 33

Question 11.
In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours, if the count was initially 5,06,000.
Solution.
Initial count of bacteria
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 34
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 35

Question 12.
A scooter was bought at ₹ 42,000. It’s value depreciated at the rate of 8% per annum. Find its value after one year.
Solution.
Initial value of the scooter
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 36
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.3 37

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Online Education NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1

In Online Education NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 12
Chapter Name Exponents and Powers
Exercise Ex 12.1
Number of Questions Solved 7
Category NCERT Solutions

Online Education NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1

Question 1.
Evaluate :
(i) \({ 3 }^{ -2 }\)
(ii) \({ -4 }^{ -2 }\)
(iii) \(({ \frac { 1 }{ 2 } ) }^{ -5 }\)
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 1
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 2

Question 2.
Simplify and express the result in power notation with positive exponent.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 3
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 4
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 5
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 6

Question 3.
Fmd the value of:
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 7
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 8
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 9
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 10
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 11

Question 4.
Evaluate
(i) \(\frac { { 8 }^{ -1 }\times { 5 }^{ 3 } }{ { 2 }^{ -4 } } \)
(ii) \(({ 5 }^{ -1 }\times { 2 }^{ -1 })\times { 6 }^{ -1 }\)
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 12

Question 5.
Find the value of m for which \({ 5 }^{ m }+{ 5 }^{ -3 }={ 5 }^{ 5 }\)
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 13
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 14

Question 6.
Evaluate :
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 15
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 16
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 17
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 18

Question 7.
Simplify:
(i) \(\frac { 25\times { t }^{ -4 } }{ { 5 }^{ -3 }\times 10\times { t }^{ -8 } } \) (t ≠ 0)
(ii) \(\frac { { 3 }^{ -5 }\times { 10 }^{ -5 }\times 125 }{ { 5 }^{ -7 }\times { 6 }^{ -5 } } \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 19
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 20
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 21
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 22

 

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Online Education NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2

In Online Education NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 14
Chapter Name Factorisation
Exercise Ex 14.2
Number of Questions Solved 5
Category NCERT Solutions

Online Education NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2

Question 1.
Factorise the following expressions:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 2
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 3
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 4
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 21

Question 2.
Factorise:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 24
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 8
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 9
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 10

Question 3.
Factorise the expressions:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 26
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 27
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 12
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 13

Question 4.
Factorise:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 14
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 15
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 16
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 17

Question 5.
Factorise the following expressions:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 18
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 19
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 20

 

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Online Education NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3

In Online Education NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 11
Chapter Name Mensuration
Exercise Ex 11.3
Number of Questions Solved 10
Category NCERT Solutions

Online Education NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3

Question 1.
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 2

Question 2.
A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpau¬lin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 3

Question 3.
Find the side of a cube whose surface area is 600 \({ cm }^{ 2 }\).
Solution.
Let the side of the cube be a cm.
Then, Total surface area of the cube = 6\({ a }^{ 2 }\)
According to the question,
6\({ a }^{ 2 }\)= 600
⇒ \({ a }^{ 2 }\) = \(\frac { 600 }{ 6 } \)
⇒ \({ a }^{ 2 }\) = 100
⇒ a = \(\sqrt { 100 } \)
⇒ a = 10 cm
Hence, the side of the cube is 10 cm.

Question 4.
Rukhsar painted the outside of the cabinet of measure 1 m x 2 m x 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 4
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 5

Question 5.
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth, and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 \({ m }^{ 2 }\) of area is painted.
How many cans of paint will she need to paint the room?
Solution.
l = 15 m
b = 10 m
h = 7 m
Surface area to be painted
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 6
Hence, she will need 5 cans of paint to paint the room.

Question 6.
Describe how the two figures at the right are alike and how they are different. Which box has a larger lateral surface area?
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 7
Solution.
Similarity → Both have the same heights.
Difference → One is a cylinder, the other is a cube;
The cylinder is a solid obtained by revolving a rectangular area about its one side whereas a cube is a solid enclosed by six square faces; a cylinder has two circular faces whereas a cube has six square faces.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 8

Question 7.
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How many sheets of metal is required?
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 9
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 10

Question 8.
The lateral surface area of a hollow cylinder is 4224 \({ cm }^{ 2 }\). It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Solution.
Lateral surface area of the hollow cylinder = 4224 \({ cm }^{ 2 }\)
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 11

Question 9.
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
Solution.
Diameter of the road roller = 84 cm
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 12
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 13

Question 10.
A company packages its milk powder in the cylindrical container whose base has a diameter of 14 cm and height 20 cm. The company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 14
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.3 15

 

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Online Education NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2

In Online Education NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 11
Chapter Name Mensuration
Exercise Ex 11.2
Number of Questions Solved 11
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2

Question 1.
The shape of the top surface of a table is a trapezium. Find its area, if its parallel sides are 1 m and 1.2 man the d perpendicular distance between them is 0.8 m.
Solution.
Area of the top surface of the table
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 1
= \(\frac { 1 }{ 2 } h(a+b)\)
= \(\frac { 1 }{ 2 } \times 0.8\times (1.2+1)\)
= \(0.88{ m }^{ 2 }\)

Question 2.
The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the another parallel side.
Solution.
Area of trapezium
= \(\frac { 1 }{ 2 } h(a+b)\)
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 2
⇒ \(34=\frac { 1 }{ 2 } \times 4(10+b)\)
⇒ \(34=2\times (10+b)\)
⇒ \(10+b=\frac { 34 }{ 2 } \)
⇒ 10 + b=17
⇒ b = 17 – 10
⇒ b = 7 cm
Hence, the length of another parallel side is 7 cm.

Question 3.
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 3
Solution.
Fence of the trapezium shaped field ABCD = 120 m
⇒ AB + BC + CD + DA = 120
⇒ AB + 48 + 17 + 40 = 120
⇒ AB + 105 = 120
⇒ AB = 120 – 105
⇒ AB = 15 m
∴ Area of the field
= \(\frac { (BC+AD)\times AB }{ 2 } \)
= \(\frac { (48+40)\times 16 }{ 2 } \) = 660 \({ m }^{ 2 }\)

Question 4.
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 4
Solution.
Area of the field
= \(\frac { 1 }{ 2 } d({ h }_{ 1 }+{ h }_{ 2 })\)
= \(\frac { 24\times (8+13) }{ 2 } \) = \(\frac { 24\times 21 }{ 2 } \)
= 12 x 21 = 252\({ m }^{ 2 }\)

Question 5.
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Solution.
Area of the rhombus
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 5
= \(\frac { 1 }{ 2 } \times { d }_{ 1 }\times { d }_{ 2 }\)
= \(\frac { 1 }{ 2 } \times 7.5\times 12\)
= 45 \({ m }^{ 2 }\)

Question 6.
Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
Solution.
Area of the rhombus
= base (b) x altitude (h) = 5
= 5 x 4.8 = 24 \({ cm }^{ 2 }\)
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 6

Question 7.
The floor of a building consists of 3,000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per \({ m }^{ 2 }\) is ₹ 4.
Solution.
Area of a tile
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 7

Question 8.
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10,500 \({ m }^{ 2 }\) and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Solution.
Let the length of the side along the road be x m. Then, the length of the side along the river is 2x m.
Area of the field = 10,500 square metres
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 8

Question 9.
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
Solution.
Area of the octagonal surface
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 9
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 10

Question 10.
There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 11
Find the area of this park using both ways. Can you suggest some other way of finding its area ?
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 12
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 13

Question 11.
Diagram of the adjacent picture frame has outer dimensions = 24 cm x 28 cm and inner dimensions 16 cm x 20 cm. Find the area of each section of the frame, if the width of each section the same.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 14
Solution.
NCERT Solutions for Class 8 Maths Chapter 11 Mensuration Ex 11.2 15

 

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NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 16
Chapter Name Playing with Numbers
Exercise Ex 16.2
Number of Questions Solved 4
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2

Question 1.
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
Solution.
Since 21y5 is a multiple of 9, its sum of digits 2 + 1+ y + 5 = 8+ y isa multiple of 9; so 8 + y is one of these numbers: 0, 9, 18, 27, 36, 45,… .
But since y is a digit, it can only be possible that 8 + y = 9. Therefore, y = 1.

Question 2.
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers to the last problem. Why is this so?
Solution.
Since 31z5 is a multiple of 9, its sum of digits 3 + 1 + z + 5 = 9 + z isa multiple of 9; so 9 + z is one of these numbers: 0, 9, 18, 27, 36, 45, … .
But since z is a digit, it can only be possible that 9 + z = 9 or 18. Therefore, z = 0 or 9.

Question 3.
If 24x is a multiple of 3, where x is a digit, what is the value of x?
(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … .
But since xis a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)
Solution.
The solution is given with question.

Question 4.
If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
Solution.
Since 31z5 is a multiple of 3, its sum of digits 3 + 1 + z + 5 = 9 + z is a multiple of 3; so 9 + z is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … .
But since z is a digit, it can only be possible that 9 + z = 9 or 12 or 15 or 18. Therefore, z = 0 or 3 or 6 or 9.

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NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 15
Chapter Name Introduction to Graphs
Exercise Ex 15.3
Number of Questions Solved 2
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3

Question 1.
Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 1
(b) Distance travelled by a car
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 2
(i) How much distance the car cover during the period 7.30 a.m. to 8 a.m.?
(ii) What was the time when the car had covered a distance of 100 km since it starts?

(c) Interest on deposits for a year.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 3
(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on? 2500 for a year.
(iii) To get an interest of ? 280 per year, how much money should be deposited?
Solution.
(a)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 4
Scale:
On horizontal axis:         2 units = 1 apple
On vertical axis:              1 unit = ₹ 5
Mark number of apples on the horizontal axis.
Mark cost (in ?) on the vertical axis.
Plot the points: (1, 5), (2, 10), (3, 15), (4, 20) and (5, 25)
Join the points.
We get a linear graph.

(b)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 5
Scale:
On horizontal axis:      2 units = 1 hour
On vertical axis:           2 units = 40 km
Mark time (in hours) on the horizontal axis.
Mark distances (in km) on the vertical axis.
Plot the points (6 a.m., 40), (7 a.m., 80) (8 a.m., 120) and (9 a.m., 160).
Join the points.
We get a linear graph.
(i) Distance covered during 7.30 a.m. to 8 a.m.
= 120 km – 100 km = 20 km
(ii) The time when the car had covered a distance of 100 km since its start was 7.30 a.m.

(c)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 6Scale:
On horizontal axis:       2 units = ₹ 1000
On vertical axis:            2 units = ₹ 80
Mark deposit (in ₹ on the horizontal axis.
Mark simple interest (in ₹) on the vertical axis.
Plot the points (1000, 80), (2000, 160), (3000, 240) (4000, 320) and (5000, 400).
Join the points.
We get a linear graph.
(i) Yes! The graph passes through the origin.
(ii) Interest on ₹ 2500 for a year = ₹ 200
(iii) To get an interest of ₹ 280 per year, ₹ 3500 should be deposited.

Question 2.
Draw a graph for the following:
(i)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 7
Is it a linear graph?
(ii)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 8
Is it a linear graph?
Solution.
(i)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 9
Scale:
On horizontal axis:     1 unit = 1 cm
On vertical axis:          1 unit = 4 cm
Mark side of the square (in cm) on the horizontal axis.
Mark perimeter (in cm) on the vertical axis.
Plot the points (2, 8), (3, 12), (3.5. 14) (5, 20) and (6, 24).
Join the points.
Yes ; it is a linear graph.

(ii)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 10
• Scale:
On horizontal axis: 2 units = 2 cm
On vertical axis: 1 unit = 2 cm
Mark side of the square (in cm) on the horizontal axis.
Mark area (in cm ) on the vertical axis.
Plot the points (2, 4) (3, 9), (4, 16), (5, 25) and (6, 36).
Join the points.
The graph we get is not linear.

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 15
Chapter Name Introduction to Graphs
Exercise Ex 15.2
Number of Questions Solved 4
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2

Question 1.
Plot the following points on a graph sheet. Verify if they lie on a line.
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(l, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 1
(a) The points lie on a line.
(b) The points lie on a line.
(c) The points do not lie on a line.

Question 2.
Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Solution.
The coordinates of the points at which this line meets the x-axis and y-axis are (5, 0) and (0, 5) respectively. See the graph given above.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 2

Question 3.
Write the coordinates of the vertices of each of these adjoining figures.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 3
Solution.
O → (0, 0)
A → (2,0)
B → (2, 3)
C → (0,3)

P → (4, 3)
Q → (6, 1)
R → (6, 5)
S → (4, 7)

K → (10, 5)
L → (7, 7)
M → (10, 8)

Question 4.
State whether True or False. Correct that is false.
(i) A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
(ii) A point whose y-coordinate is zero ‘ and x-coordinate is 5 will lie on y-axis.
(iii) The coordinates of the origin are (0, 0).
Solution.
(i) True
(ii) False; A point whose y-coordinate is zero and x-coordinate is 5 will lie on x-axis.
(iii) True

 

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NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 14
Chapter Name Factorisation
Exercise Ex 14.4
Number of Questions Solved 21
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4

Find and correct the errors in the following mathematical statements.
Question 1.
4(x – 5) = 4x – 5
Solution.
4(x – 5) = 4x – 20

Question 2.
x(3x + 2) = \({ 3x }^{ 2 }+2\)
Solution.
x(3x + 2) = \({ 3x }^{ 2 }+2x\)

Question 3.
2x + 3y = 5xy
Solution.
2x + 3y = 2x + 3y

Question 4.
x + 2x + 3x = 5x
Solution.
x + 2x + 3x = 6x

Question 5.
5y + 2y + y – 7y = 0
Solution.
5y + 2y + y – 7y – y

Question 6.
3x + 2x = \({ 5x }^{ 2 }\)
Solution..
3x + 2x = 5x

Question 7.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 2x }^{ 2 } + 8x + 7 \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 4x }^{ 2 } + 8x + 7 \)

Question 8.
\({ \left( 2x \right) }^{ 2 } + 5x = 4x + 5x = 9x \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 5x = { 4x }^{ 2 } + 5x \)

Question 9.
\({ \left( 3x+2 \right) }^{ 2 } = { 3x }^{ 2 } + 6x + 4. \)
Solution.
\({ \left( 3x+2 \right) }^{ 2 } = { 9x }^{ 2 }+ 12x + 4. \)

Question 10.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 2

Question 11.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 9 \)
Solution.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 2(y)(3) + { 3 }^{ 2 }\)
= \({ y }^{ 2 } – 6y + 9 \)
and not equal to \({ y }^{ 2 } – 9 \)

Question 12.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 25 \)
Solution.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 2(z) (5) + { 5}^{ 2 }\)
= \({ z }^{ 2 } + 10z + 25 \)
and not equal to \({ z }^{ 2 } + 25 \)

Question 13.
\(\left( 2a+36 \right) \left( a-b \right) = { 2a }^{ 2 }-{ 3b }^{ 2 }\)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 3
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 4

Question 14.
\(\left( a+4 \right) \left( a+2 \right) = { a}^{ 2 } + 8 \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 5

Question 15.
\(\left( a-4 \right) \left( a-2 \right) = { a}^{ 2 }-8 \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 6

Question 16.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =0\)
Solution.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =1\) and not equal to 0

Question 17.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =1+1=2\)
Solution.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } +\frac { 1 }{ { 3x }^{ 2 } } \)
=\(1+\frac { 1 }{ { 3x }^{ 2 } }\) and not equal to 1 + 1 = 2

Question 18.
\(\frac { 3x }{ 3x+2 } =\frac { 1 }{ 2 } \)
Solution.
\(\frac { 3x }{ 3x+2 } =\frac { 3x }{ 3x+2 } \) and not equal to \(\frac { 1 }{ 2 }\)

Question 19.
\(\frac { 3 }{ 4x+3 } =\frac { 1 }{ 4x } \)
Solution.
\(\frac { 3 }{ 4x+3 } =\frac { 3 }{ 4x+3 } \) and not equal to \(\frac { 1 }{ 4x }\)

Question 20.
\(\frac { 4x+5 }{ 4x } =5\)
Solution.
\(\frac { 4x+5 }{ 4x } =\frac { 4x }{ 4x } +\frac { 5 }{ 4x } =1+\frac { 5 }{ 4x } \) and not equal to 5

Question 21.
\(\frac { 7x+5 }{ 5 } =7x\)
Solution.
\(\frac { 7x+5 }{ 5 } =\frac { 7x }{ 5 } +\frac { 5 }{ 5 } =\frac { 7x }{ 5 } +1\) and not equal to 7x

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 14
Chapter Name Factorisation
Exercise Ex 14.3
Number of Questions Solved 5
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3

Question 1.
Carry out the following divisions:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 2
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 3
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 4
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 5

Question 2.
Divide the given polynomial by the given monomial:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 6
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 7
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 8
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 9

Question 3.
Work out the following divisions:
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 10
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 11
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 12

Question 4.
Divide as directed.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 13
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 14

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 15

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 16

Question 5.
Factorise the expressions and divide them as directed.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 17
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 18
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 19
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 20
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 21
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 22
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 23
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 24
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 25

 

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NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2.

Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 13
Chapter Name Direct and Indirect Proportions
Exercise Ex 13.2
Number of Questions Solved 11
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2

Question 1.
Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time is taken for a journey and the distance traveled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time is taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
Solution.
(i) The number of workers on jobs and the time to complete the job are in inverse proportion.
(ii) The time is taken for a journey and the distance traveled in a uniform speed are not in inverse proportion.
(iii) Area of cultivated land and the crop harvested are not in inverse proportion.
(iv) The time taken for a fixed journey and the speed of the vehicle are in inverse proportion.
(v) The population of a country and the area of land per person are in inverse proportion.

Question 2.
In a Television game show, the prize money of  1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 2

Question 3.
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 3
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 4
(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in verse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
Solution.
Let the angle (in degree) between a pair of consecutive spokes be \({ y }_{ 3 }\), \({ y }_{ 4 }\) and \({ y }_{ 5 }\) respectively. Then,
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 5
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 6

Question 4.
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
Solution.
Suppose that each would get \({ y }_{ 2 }\) sweets.
Thus, we have the following table.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 7

Question 5.
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
Solution.
Suppose that the food would last for \({ y }_{ 2 }\) days. We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 8

Question 6.
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
Solution.
Suppose that they take \({ y }_{ 2 }\) days to complete the job. We have the following table
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 9

Question 7.
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 10v
Solution.
Suppose that \({ y }_{ 2 }\) boxes would be filled. We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 11

Question 8.
A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
Solution.
Suppose that \({ x }_{ 2 }\) machines would be required. We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 12
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 14

Question 9.
A car takes 2 hours to reach a destination by traveling at a speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
Solution.
Let it take \({ y }_{ 2 }\) hours. We have the following table:
sol.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 15

Question 10.
Two persons could fit new windows in a house in 3 days.
(i) One of the persons fell ill before the work started. How long would the job take now?
(ii) How many persons would be needed to fit the windows in one day?
Solution.
(i) Let the job would take \({ y }_{ 2 }\) days. We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 16
Clearly, more the number of persons, lesser would be the number of days to do the job. So, the number of persons and number of days vary in inverse proportion.
So, 2 x 3 = 1 x \({ y }_{ 2 }\)
⇒ \({ y }_{ 2 }\) = 6
Thus, the job would now take 6 days.

(ii) Let \({ y }_{ 2 }\) persons be needed. We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 17
Clearly, more the number of persons, lesser would be the number of days to do the job. So, the number of persons and number of days vary in inverse proportion.
So, 3 x 2 = 1 x \({ y }_{ 3 }\)
⇒ \({ T }_{ 2 }\) = 6
Thus, 6 persons would be needed.

Question 11.
A school has 8periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?
Solution.
Let each period be \({ y }_{ 2 }\) minutes long.
We have the following table:
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 18
We note that more the number of periods, lesser would be the length of each period. Therefore, this is a case of inverse proportion.
So, 8 x 45 = 9 x \({ y }_{ 2 }\)
⇒ \({ y }_{ 2 }=\frac { 8\times 45 }{ 9 } \)
⇒ \({ y }_{ 2 }\) = 40
Hence, each period would be 40 minutes long.

We hope the NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 13 Direct and Indirect Proportions Ex 13.2, drop a comment below and we will get back to you at the earliest.