Category: ICSE

Selina Publishers Concise Mathematics Class 6 ICSE Solutions

• Chapter 1 Number System (Consolidating the Sense of Numberness)
• Chapter 2 Estimation
• Chapter 3 Numbers in India and International System (With Comparison)
• Chapter 4 Place Value
• Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)
• Chapter 6 Negative Numbers and Integers
• Chapter 7 Number Line
• Chapter 8 HCF and LCM
• Chapter 9 Playing with Numbers
• Chapter 10 Sets
• Chapter 11 Ratio
• Chapter 12 Proportion (Including Word Problems)
• Chapter 13 Unitary Method
• Chapter 14 Fractions
• Chapter 15 Decimal Fractions
• Chapter 16 Percent (Percentage)
• Chapter 17 Idea of Speed, Distance and Time
• Chapter 18 Fundamental Concepts
• Chapter 19 Fundamental Operations (Related to Algebraic Expressions)
• Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)
• Chapter 21 Framing Algebraic Expressions (Including Evaluation)
• Chapter 22 Simple (Linear) Equations (Including Word Problems)
• Chapter 23 Fundamental Concepts
• Chapter 24 Angles (With their Types)
• Chapter 25 Properties of Angles and Lines (Including Parallel Lines)
• Chapter 26 Triangles (Including Types, Properties and Constructions)
• Chapter 27 Quadrilateral
• Chapter 28 Polygons
• Chapter 29 The Circle
• Chapter 30 Revision Exercise Symmetry (Including Constructions on Symmetry)
• Chapter 31 Recognition of Solids
• Chapter 32 Perimeter and Area of Plane Figures
• Chapter 33 Data Handling (Including Pictograph and Bar Graph)
• Chapter 34 Mean and Median

Selina Publishers Concise Biology Class 7 ICSE Solutions

• Chapter 1 Plant And Animal Tissues
• Chapter 2 Classification of Plants
• Chapter 3 Classification of Animals
• Chapter 4 Photosynthesis and Respiration
• Chapter 5 Excretion in Humans
• Chapter 6 Nervous System
• Chapter 7 Allergy

Selina Publishers Concise Chemistry Class 7 ICSE Solutions

• Chapter 1 Matter and Its Composition
• Chapter 2 Physical and Chemical Changes
• Chapter 3 Elements, Compounds and Mixtures
• Chapter 4 Atoms, Molecules and Radicals
• Chapter 5 Language of Chemistry
• Chapter 6 Metals and Non-metals
• Chapter 7 Air and Atmosphere

Selina Publishers Concise Mathematics Class 7 ICSE Solutions

• Chapter 1 Integers
• Chapter 2 Rational Numbers
• Chapter 3 Fractions (Including Problems)
• Chapter 4 Decimal Fractions (Decimals)
• Chapter 5 Exponents (Including Laws of Exponents)
• Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)
• Chapter 7 Unitary Method (Including Time and Work)
• Chapter 8 Percent and Percentage
• Chapter 9 Profit, Loss and Discount
• Chapter 10 Simple Interest
• Chapter 11 Fundamental Concepts (Including Fundamental Operations)
• Chapter 12 Simple Linear Equations (Including Word Problems)
• Chapter 13 Set Concepts (Some Simple Divisions by Vedic Method)
• Chapter 14 Lines and Angles (Including Construction of angles)
• Chapter 15 Triangles
• Chapter 16 Pythagoras Theorem
• Chapter 17 Symmetry (Including Reflection and Rotation)
• Chapter 18 Recognition of Solids (Representing 3-D in 2-D)
• Chapter 19 Congruency: Congruent Triangles
• Chapter 20 Mensuration
• Chapter 21 Data Handling
• Chapter 22 Probability

Selina Publishers Concise Biology Class 8 ICSE Solutions

• Chapter 1 Transportation in Plants
• Chapter 2 Reproduction in Plants
• Chapter 3 Reproduction in Humans
• Chapter 4 Ecosystems
• Chapter 5 Endocrine System and Adolescence
• Chapter 6 The Circulatory System
• Chapter 7 Nervous System
• Chapter 8 Diseases and First Aid
• Chapter 9 Food Production

Selina Publishers Concise Chemistry Class 8 ICSE Solutions

• Chapter 1 Matter
• Chapter 2 Physical and Chemical Changes
• Chapter 3 Elements, Compounds and Mixtures
• Chapter 4 Atomic Structure
• Chapter 5 Language of Chemistry
• Chapter 6 Chemical Reactions
• Chapter 7 Hydrogen
• Chapter 8 Water
• Chapter 9 Carbon and Its Compounds

Selina Publishers Concise Physics Class 8 ICSE Solutions

• Chapter 1 Matter
• Chapter 2 Physical Quantities and Measurement
• Chapter 3 Force and Pressure
• Chapter 4 Energy
• Chapter 5 Light Energy
• Chapter 6 Heat Transfer
• Chapter 7 Sound
• Chapter 8 Electricity

Selina Publishers Concise Physics Class 7 ICSE Solutions

• Chapter 1 Physical Quantities and Measurement
• Chapter 2 Motion
• Chapter 3 Energy
• Chapter 4 Light Energy
• Chapter 5 Heat
• Chapter 6 Sound
• Chapter 7 Electricity and Magnetism

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:

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:

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:

Question 4.
The cost of 35 envelops is ₹ 105. How many envelops can be bought for ₹ 90?
Solution:

Question 5.
If the cost of 8 cans of juice is ₹ 280, then what will be the cost of 6 cans of juice?
Solution:

Question 6.
For ₹ 378, 9 cans of juice can be bought, then how many cans of juice can be bought for ₹ 504?
Solution:

Question 7.
A motorbike travels 425 km in 5 hours. How much distance will be covered by it in 3.2 hours?
Solution:

Question 8.
If the cost of a dozen identical articles is ₹ 672, what will be the cost of 18 such articles?
Solution:

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:

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:

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:

Question 12.
Rohit buys 10 pens for ₹ 150 and Manoj buys 14 pens for ₹ 168. Who got the pens cheaper?
Solution:

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:

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:

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:

Question 2.
A made 84 runs in 6 overs and B made 126 runs in 7 overs. Who made more runs per over?
Solution:

Question 3.
Geeta types 108 words in 6 minutes. How many words would she type in half an hour?
Solution:

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:

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:

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:

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:

Question 8.
If John walks 250 steps to cover a distance of 200 metres, find the distance covered by him in 350 steps.
Solution:

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:

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

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:

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:

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:

Question 4.
The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.
Solution:

Question 5.
Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.
Solution:

Question 6.
Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.
Solution:

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:

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:

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:

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:

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:

Question 12.
Make set of all possible proportions from the numbers 15, 18, 35 and 42.
Solution:

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:

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:

Question 3.
Find the mean proportion between
(i) 3 and 27
(ii) 0.06 and 0.96
Solution:

Question 4.
Find the third proportional to :
(i) 36, 18
(ii) 5.25, 7
(iii) ₹ 1.60, ₹ 0.40
Solution:

Question 5.
The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.
Solution:

Question 6.
If (4x + 3y) : (3x + 5y) = 6 : 7, find :
(i) x : y
(ii) x, if y = 10
(iii) y, if x = 27
Solution:
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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:

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:

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:

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:

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:

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:

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:

Question 7.
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?
Solution:

Question 8.
Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?
Solution:

Question 9.
10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x
Solution:

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:

Question 11.
If 4, x and 9 are in continued proportion, find the value of x.
Solution:

Question 12.
If 25, 35 and x are in continued proportion, find the value of x.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

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

Solution:

Question 2.
A field is 80 m long and 60 m wide. Find the ratio of its width to its length.
Solution:

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:

Question 4.
Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years?
Solution:

Question 5.
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm?
Solution:

Question 6.
Find the ratio between 3.5 m, 475 cm and 2.8 m.
Solution:

Question 7.
Find the ratio between 5 dozen and 2 scores. [1 score = 20]
Solution:

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:

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:

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:

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:

Question 5.
Two numbers are in the ratio 9 : 2. If the smaller number is 320, find the larger number.
Solution:

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:

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:

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:

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:

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:

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:

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:

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:

Question 2.
Divide 72 in the ratio \(2\frac { 1 }{ 2 } :1\frac { 1 }{ 2 }\)
Solution:

Question 3.
Divide 81 into three parts in the ratio 2 : 3 : 4.
Solution:

Question 4.
Divide Rs 10,400 among A, B and C in the ratio \(\frac { 1 }{ 2 } :\frac { 1 }{ 3 } :\frac { 1 }{ 4 } \)
Solution:

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:

Question 6.
The angles of a triangle are in the ratio 3 : 7 : 8. Find the greatest and the smallest angles.
Solution:

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:

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:

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:

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:

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

Question 1.
Which ratio is greater:

Solution:

Question 2.
Which ratio is smaller :

Solution:

Question 3.
Increase 95 in the ratio 5 : 8.
Solution:

Question 4.
Decrease 275 in the ratio 11 : 7.
Solution:

Question 5.
Decrease 850 in the ratio 17 : 6 and then increase the result in the ratio 5 : 9.
Solution:

Question 6.
Decrease 850 in the ratio 17 : 6 and then decrease the resulting number again in 4 : 3.
Solution:

Question 7.
Increase 1200 in the ratio 2 : 3 and then decrease the resulting number in the ratio 10 : 3.
Solution:

Question 8.
Increase 1200 in the ratio 3 : 7 and then increase the resulting number again in the ratio 4 : 7.
Solution:

Question 9.
The number 650 is decreased to 500 in the ratio a : b, find the ratio a : b.
Solution:

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