# Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions

Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions Chapter-8. We provide step by step Solutions of Exercise / lesson-8 Ratio and Proportion ICSE Class-6th ML Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe- 8.1, Exe-8.2, Exe- 8.3, Exe-8.4, Exe- 8.5,  Objective Type Questions  (includes: Mental Maths, MCQs, Value Based Questions HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Maths.

## Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions Chapter-8

–: Select Topic :–

Exercise 8.1 ,

Exercise-8.2,

Exercise-8.3,

Exercise-8.4,

Exercise-8.5,

Objective Type Questions,

Mental Maths,

Multiple Choice Questions ,(MCQ)

Value Based Question

HOTS

### Exercise-8.1, Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions Chapter-8

Question 1.

Express the following ratios in simplest form:
(i) 20 : 40
(ii)40 : 20
(iii) 81 : 108
(iv) 98 : 63

Question 2

Fill in the missing numbers in the following equivalent ratios:

Question 3

Find the ratio of each of the following in simplest form :
(i) 2.1 m to 1.2 m
(ii) 91 cm to 1.04m
(iii) 3.5 kg to 250gm
(iv) 60 paise to 4 rupees
(v) 1 minute to 15 seconds
(vi) 15 mm to 2 cm

(i) 2.1 m : 1.2 m- =$\frac{2.1}{1.2}=\frac{21}{12} \times \frac{10}{10}=\frac{7}{4}$ = 7 : 4
(ii) 91 cm : 1.04cm or 1.04 × 100 or 104 cm
91 cm : 104 cm = $\frac{91}{104}$ = 7 : 8
(iii) 3.5 kg : 250 gm or 3.5 × 1000gm : 250 gm
$\frac{3500}{250}=\frac{14}{1}=14 : 1$
(iv) 60 paise : 4 rupees
1 rupees = 100 paise
∴ 60 paise

(v) 1 minute : 15 seconds
60 seconds = 1 minute
1 minute : 15 seconds

(vi) 15 mm : 20 cm
10 mm = 1 cm

Question 4.

The length and the breadth of a rectangular park are 125 m and 60 m respectively. What is the ratio of the length to the breadth of the park?

Length of rectangular park = 125 m
Breadth of rectangular park = 60 m
∴ Ratio of the length to the breadth of park is
$\frac{125}{60}=\frac{25}{12}=25 : 12$

Question 5

The population of village is 4800. If the numbers of females is 2160, find the ratio of males to that of females.

Population of village = 4800
No. of females = 2160
No. of males = 4800 – 2160 = 2640
No. of males : No. of females
2640 : 2160
$\frac{2640}{2160}=\frac{264}{216}=\frac{11}{9}=11 : 9$

Question 6.
In a class, there are 30 boys and 25 girls. Find the ratio of the numbers of
(i) boys to that of girls.
(ii) girls to that of total number of students.
(iii) boys to that of total numbers of students.

Boys = 30, girls = 25
Total students = 30 + 25 = 55
(i) boys : girls = 30 : 25 ⇒ $\frac{30}{25}=\frac{6}{5}=6 : 5$
(ii) girls : Total No. of students
$25 : 55 \Rightarrow \frac{25}{55}=\frac{5}{11}=5 : 11$
(iii) Boys : Total No. of students
$30 : 55 \Rightarrow \frac{30}{55}=\frac{6}{11}=6 : 11$

Question 7

In a year, Reena earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of
(i) money she earns to the money she saves.
(ii) money that she saves to the money she spends.

(i) Ratio of money that Reena earns to the money she saves

(ii) Money that she spends
= ₹ 1,50,000 – ₹50,000 = ₹1,00,000
∴ Ratio of money she saves to the money she spends

Question 8

The monthly expenses of a student have increased from ₹350 to ₹500. Find the ratio of
(i) increase in expenses and original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increased in expenses.

Original exp. = ₹350
Increased exp. = ₹500
Increased in exp. = 500 – 350 = ₹150
(i) Increased in exp : original exp.
$150 : 350 \Rightarrow \frac{150}{350}=\frac{15}{35}=\frac{3}{7}=3 : 7$
(ii) Original exp. : Increased exp.
$350 : 500 \Rightarrow \frac{350}{500}=\frac{35}{50}=\frac{7}{10}=7 : 10$
(iii) Increased exp : Increase in exp.
$500 : 150 \Rightarrow \frac{500}{150}=\frac{50}{15}=\frac{10}{3}=10 : 3$

Question 9

Mr Mahajan and his wife are both school teachers and earn ₹20900 and ₹ 18700 per month respectively. Find the ratio of
(i) Mr Mahajan’s income to his wife’s income.
(ii) Mrs Mahajan’s income to the total income of both.

(i) Ratio in Mr Mahajan’s income and his wife
= 20900 : 18700
$\frac{20900}{18700}=\frac{19}{17}=19 : 17$

(ii) Mrs Mahajan’s income to the total income of both
Earning of Mrs Mahajan = ₹20900
and his wife = ₹ 18700
Total income = ₹39,600
Mrs Mahajan’s income to the total income of both
$\frac{18700}{39600}=\frac{17}{36}=17 : 36$

Question 10

Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.

Question 11

Divide ₹ 560 between Ramu and Munni in the ratio 3 : 2.

Total amount = ₹ 560
Ratio in Ramu and Munni = 3 : 2
Sum of ratios = 3 + 2 = 5
Ramu shares = ₹$\frac{560 \times 3}{5}$ = ₹336
Munni shares = ₹ $\frac{560 \times 3}{5}$= ₹224

Question 12

Two people invested ₹ 15000 and ₹25000 respectively to start a business. They decided to share the profits in the ratio of their investments. If their profit is ₹ 12000, how much does each get?

Total investment = 15000 + 25000 = 40000
Investment of 1 st person = $\frac{15000}{40000}=\frac{3}{8}$
Investment of 2nd person = $1-\frac{3}{8}=\frac{5}{8}$
Total profit = ₹ 12000
Profit of 1st person = $\frac{3}{8}$ × ₹12000 = ₹4500
Profit of 2nd person = ₹12000 – ₹4500 = ₹7500

Question 13

The ratio of Ankur’s money to Roma’s money is 9 : 11. if Ankur has ₹540, how much money does Roma have?

Ratio of Ankur’s two Roma’s money = 9 : 11
Ankur has money = ₹540

Question 14

The ratio of weights of tin and zinc in on alloy is 2 : 5. How much zinc is there in 31.5 g of alloy?

## Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions Exercise- 8.2,

Question 1

Check whether the given two ratios form a proportion or not:
(i) 4 : 6 and 12 : 18
(ii) 15:45 and 40 :120
(iii) 14 : 4 and 18 : 6
(iv) 12 : 18 and 28 : 12

Question 2

Write true (T) or false (F) against each of the following statements:
(i) 16 : 24 = 20 : 30
(ii) 16 : 24 = 30 : 20
(iii) 21 : 6 :: 35 : 10
(iv) 5.2 : 3.9 :: 3 :4

(i) 16 : 24 = 20 : 30
2 : 3 = 2 : 3 True
(ii) 16 : 24 = 30 : 20
2 : 3 = 3 : 2 False
(iii) 21 : 6 :: 35 : 10
21 : 6 = 35 : 10
7 : 2 = 7 : 2 True
(iv) 5.2 : 3.9 :: 3 : 4

Question 3.

Find which of the following are in proportion:
(i) 12, 16, 6, 8
(ii) 2, 3, 4, 5
(iii) 18, 10, 9, 5
(iv) 18, 9, 10, 5

(i) 12, 16, 6, 8
12: 16 :: 6 : 8
$\Rightarrow \frac{12}{16}=\frac{6}{8}$
12 × 8 = 16 × 6 ⇒ 96 = 96
∴ 12 : 16 :: 6 : 8 are in proportion
(ii) 2, 3, 4, 5
2 : 3 :: 4 : 5
$\Rightarrow \frac{2}{3}=\frac{4}{5}$
2 × 5 = 3 × 4 ⇒ 10 = 12 not in proportion
(iii) 18, 10, 9, 5
18 : 10 : : 9 : 5
$\Rightarrow \frac{18}{10}=\frac{9}{5}$
∴ 18 × 5 = 10 × 9 ⇒ 90 = 90
∴ 18 : 10 :: 9 : 5 are in proportion
(iv) 18, 9, 10, 5
18 : 9 :: 10 : 5
$\Rightarrow \frac{18}{9}=\frac{10}{5}$
18 × 5 = 9 × 10
⇒ 90 = 90
∴ 18 : 9 :: 10 : 5 are in proportion

Question 3

Are the following statements true?
(i) 39 kg : 36 kg = 26 men : 24 men
(ii) 45 km : 60 km = 12 hours : 15 hours
(iii) 40 people : 200 people = ₹1000 : ₹5000
(iv) 7.5 litres: 15 litres = 15 children: 30 children

(i) 12, 16, 6, 8
12: 16 :: 6 : 8
$\Rightarrow \frac{12}{16}=\frac{6}{8}$
12 × 8 = 16 × 6 ⇒ 96 = 96
∴ 12 : 16 :: 6 : 8 are in proportion
(ii) 2, 3, 4, 5
2 : 3 :: 4 : 5
$\Rightarrow \frac{2}{3}=\frac{4}{5}$
2 × 5 = 3 × 4 ⇒ 10 = 12 not in proportion
(iii) 18, 10, 9, 5
18 : 10 : : 9 : 5
$\Rightarrow \frac{18}{10}=\frac{9}{5}$
∴ 18 × 5 = 10 × 9 ⇒ 90 = 90
∴ 18 : 10 :: 9 : 5 are in proportion
(iv) 18, 9, 10, 5
18 : 9 :: 10 : 5
$\Rightarrow \frac{18}{9}=\frac{10}{5}$
18 × 5 = 9 × 10
⇒ 90 = 90
∴ 18 : 9 :: 10 : 5 are in proportion

Question 4

Are the following statements true?
(i) 39 kg : 36 kg = 26 men : 24 men
(ii) 45 km : 60 km = 12 hours : 15 hours
(iii) 40 people : 200 people = ₹1000 : ₹5000
(iv) 7.5 litres: 15 litres = 15 children: 30 children

Question 5

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms when the ratios form a proportion. .
(i) 25 cm : 1 m and ₹40 : ₹ 160
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
(iii) 2 kg : 80 kg and 30 sec : 5 minutes
(iv) 200 g : 2.5 kg and ₹4 : ₹50

### ML Aggarwal ICSE Maths APC Solutions Class-6 Exercise- 8.3Ratio and Proportion

Question 1

If the cost of 9 m cloth is ₹378, find the cost of 4 m cloth.

∵ Cost of 9 m of cloth = ₹378
∴ Cost of 1 m of cloth = ₹ $\frac{378}{9}$ = ₹42
∴ Cost of 4 m cloth = ₹42 × 4 = ₹168

Question 2.
The weight of 36 books is 12 kg. What is weight of 75 such books?

∵ Weight of 36 books = 12 kg
∴Weight of 1 book = $\frac{128}{36}$ kg = $\frac{1}{3}$ kg
∴Weight of 75 books = $\frac{1}{3}$ × 75 = 25 kg

Question 3

Five pens cost ₹115. How many pens can you buy in ₹207?

₹115 is cost of 5 pens 5
₹ 1 is cost of = $\frac{5}{115}$ pens
∴ ₹207 is cost of
$=\frac{207 \times 5}{115}=\frac{207}{23}=9$ pens

Question 4

A car consumes 8 litres of petrol in covering a distance of 100 km. How many kilometres will it travel in 26 litres of petrol?

8 litre of petrol consumes for = 100 km
Then 26 litre of petrol consumes for
$\frac{26 \times 100}{8}=\frac{1300}{4}=325 \mathrm{km}$

Question 5.

A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?

∵ Diesel required for covering a distance of 594 km = 108 litres
∴ Diesel required for covering a distance of 1 km = $\frac{108}{594}$ litre
∴ Diesel required for covering a distance of 1650 km = $\frac{108}{594} \times 1650$ litres
$=\frac{2}{11} \times 1650=2 \times 150=300$ litres
Hence, 300 litres of diesel will be required by the truck to cover a distance of 1650km.

Question 6

A transport company charges ₹5400 to carry 80 quintals of weight. What will it charge to carry 126 quintals of weight (same distance)?

Charges of 80 quintals of weight = ₹5400
∴ Charges of 1 quintal = ₹ $\frac{5400}{80}$
and charges of 126 quintals
= ₹ $\frac{5400 \times 126}{80}=\frac{135 \times 126}{2}$
= 135 × 63 = ₹8505

Question 7.
42 metres of cloth is required to make 20 shirts of the same size. How much cloth will be required to make 36 shirts of that size?

For 20 shirts cloth required = 42 m
∴ Cloth required for making 1 shirt = $\frac{42}{20}$ m
∴ For 36 shirts cloth required will be
$=\frac{42 \times 36}{20}=\frac{18 \times 42}{10}=\frac{176}{10}=75.6 \mathrm{m}$

Question 8.
Cost of 5 kg of rice is ₹107.50.
(i) What will be the cost of 8 kg of rice?
(ii) What quantity of rice can be purchased in ₹64.5?

(i) Cost of 5 kg of rice = ₹107.50
∴ Cost of 1 kg of rice = ₹ $\frac{107.50}{5}$ = ₹21.5
∴ Cost of 8 kg of rice = ₹21.5 × 8 = ₹172

(ii) ∵ In ₹107.50, the quantity of rice that can be purchased = 5 kg
∴ In ₹1, the quantity of rice that can be phased = $\frac{5}{107.50} \times 54.5$ kg
∴ In ₹64.5, the quantity of rice that can be purchased = $\frac{5}{107.50} \times 54.5$
$\frac{5}{10750} \times 100 \times \frac{545}{10}=3 \mathrm{kg}$

Question 9

Cost of 4 dozen bananas is ₹ 180. How many bananas can be purchased for ₹37.50?

1 dozen contains = 12 items
∴ 4 dozens contains =12 x 4 items = 48 items
Cost of 4 dozen bananas = ₹180
That means cost of 48 bananas = ₹180
∴ Number of bananas that can be purchased for ₹1 = $\frac{48}{180}$
∴ Number of bananas that can be purchased for ₹37.50
$\frac{48}{180} \times 37.50=\frac{48}{180} \times \frac{3750}{100}=10$

Question 10

Aman purchases 12 pens for ₹156 and Payush buys 9 pens for ₹1108. Can you say who got the pens cheaper?

For Aman
∵ Cost of 12 pens = ₹156
∴ Cost of 1 pen = ₹ $\frac{156}{12}$ = ₹ 13
For Payush
∴ Cost of 9 pens = ₹108
∴ Cost of 1 pen = ₹$\frac{108}{9}$ = ₹12
So, Payush got the pens cheaper.

Question 11.
Rohit made 42 runs in 6 overs and Virat made 63 runs in 7 overs. Who made more runs per over?

For Rohit
∵ Runs made in 6 overs = 42
∴ Runs made per over = $\frac{42}{6}$ = 7
For Virat
∵ Runs made in 7 overs = 63
∴ Runs made per over = $\frac{63}{7}$ = 9
So, Virat made more runs per over.

Question 12

A bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then find the ratio of the distance travelled by them in one hour.

A bus travel in 4 hours = 160 km
∴ Distance covered by bus in 1 hour
$\frac{160}{4}$ = 40 km
A train travel in 5 hours = 320 km
∴ Distance covered by train in 1 hour
$\frac{320}{5} \mathrm{km}=64 \mathrm{km}$
Ratio in their speed = 40 : 64 = 5 : 8

### Exercise-8.4, Ratio and Proportion Class-6 ML Aggarwal ICSE Maths APC Solutions

Question 1

Find the value of:

Question 2

In a class of 60 student, 45% are girls. Find the number of boys in the class.

Total student = 60
% of girls = 45%
No. of boys = ?
No. of girls = $60 \times \frac{45}{100}=\frac{6 \times 45}{10}=27$ girls
No. of boys = Total students – No. of girls = 60 – 27 = 33 boys

Question 3.
Mr. Malkani saves 22% of his salary every month. If his salary is ₹ 12750 per month, what is his expenditure?

Total salary = ₹ 12750
Saving = 22%
∴ Total savings = 22% of ₹ 12750
= ₹ 12750 × $\frac{22}{100}$ = ₹2805
∴ Total expenditure = ₹ 12750 – ₹2805 = ₹9945

Question 4.
On a rainy day, 94% of the students were present in a school, if the number of students absent on that day was 174, find the total strength of the school.

Total % age of students = 100
Student present = 94%
Students absent = (100- 94) = 6%
Let, the total number of students in school = x
$6 \% \text { of } x=174 \Rightarrow \frac{6}{100} \times x=174$
$\Rightarrow x=174 \times \frac{100}{6} \Rightarrow x=29 \times 100=2900$
∴ Total strength of the school = 2900

### Ratio and Proportion Exe-8.5 Class-6 ML Aggarwal ICSE Maths APC Solutions

Question 1

The speed of a car is $105 \frac{1}{5}$ km/h, find the distance covered by it in $3 \frac{3}{5}$ hours.

Speed of a car = $105 \frac{1}{5}$ km/h
Distance covered by car in = $3 \frac{3}{5}$ hours
= Speed × Time

Question 2.
If the speed of a car is 50.4 km/h, find the distance covered in 3.6 hours.

Speed of a car = 50.4 km/h
∴ Distance covered in 3.6 hours
= Speed × Time
= (50.4 × 3.6) km/h
= 181.44 km

Question 3.

If a car covers a distance of 201.25 km in 3.5 hours, find the speed of the car.

Distance covered by the car = 201.25 km
and time consumed by car = 3.5 hours
∴ The speed of car = $\frac{\text { Distance }}{\text { Time }}$
$\frac{201.25}{3.5}$ km/h = 57.5 km/h

### Chapter-8 Ratio and Proportion Objective Type Questions Class-6 ML Aggarwal

#### Mental Maths

Question 1.

Fill in the blanks:
(i) In the ratio 3 : 5, the first term is …………. and second term is ………..
(ii) In a ratio, the first term is also called ……….. and second term is also called …….
(iii) If two terms of a ratio have no common factor (except 1), then the ratio is said to be in …….
(iv) To simplify a ratio, we divide the two terms by their …….
(v) The simplest form of the ratio 8 : 12 is ……
(vi) 90 cm : 1.5 m = ……….
(vii) Method of comparison of two quantities of the same kind (in same units) by division is known as …………
(viii) When two ratios are equal, they are said to be in ………
(ix) When four quantities are in proportion, then the product of ………… is equal to product of middle terms.
(x) 4.5 omo is equal to ………

(i) In the ratio 3 : 5, the first term is 3 and second term is 5.
(ii) In a ratio, the first term is also called antecedent and second term is also called consequent.
(iii) If two terms of a ratio have no common factor (except 1), then the ratio is said to be in simplest form.
(iv) To simplify a ratio, we divide the two terms by their H.C.F.
(v) The simplest form of the ratio 8 : 12 is 2 : 3.
(vi) 90 cm : 1.5 m = 3 : 5.
(vii) Method of comparison of two quantities of the same kind (in same units) by division is known as ratio.
(viii)When two ratios are equal, they are said to be in proportion.
(ix) When four quantities are in proportion, then the product of extreme terms is equal to product of middle terms.
(x) 4.5 of ₹40 is equal to ₹1.80.

Question 2

State whether the following statemtns are true (T) or false (F):
(i) Ratio exists only between two quantities of the same kind.
(ii) Ratio has no units.
(iii) If a ≠ b, then the ratio a: bis different from the ratio b : a.
(iv) If we multiply or divide both terms of a ratio by the same non-zero number, then the ratio remains the same.
(v) The ratio a: b is said to be in simplest form if HCF of a and b is 1.
(vi) In some situations, comparison of two quantities (of same kind) by difference does not make much sense.

(i) Ratio exists only between two quantities of the same kind. True
(ii) Ratio has no units. True
(iii) If a ≠ b, then the ratio a : b is different from the ratio b : a. True
(iv) If we multiply or divide both terms of a ratio by the same non-zero number, then the ratio remains the same. True
(v) The ratio a: bis said to be in simplest form if HCF of a and b is 1. True
(vi) In some situations, comparison of two quantities (of same kind) by difference does not make much sense. True

#### Multiple Choice Question (MCQ), Ratio and Proportion Chapter-8 Class-6 ML Aggarwal Solutions

Question 3

Choose the correct answer from the given four options (3 to 18):
Question 3.
A ratio equivalent to 5 : 7 is
(a) 10:21
(b) 15 : 14
(c) 20 : 28
(d) 25 : 49

5 : 7
$\Rightarrow \frac{5}{7} \times \frac{4}{4}=\frac{20}{28}=20 : 28$ (c)

Question 4

The ratio 384 : 480 in the simplest form is
(a) 2 : 5
(b) 3 : 5
(c) 5 : 4
(d) 4 : 5

384 : 480
Dividing by 96, we get
$=\frac{384}{96} : \frac{480}{96} \Rightarrow 4 : 5$ (d)

Question 5.
The ratio of 20 minutes to 1 hour is
(a) 20 : 1
(b) 1 : 3
(c) 1 : 4
(d) 2 : 5

20 min : 1 hour
20 min : 60 minutes
= 20 : 60
Divide both terms by
$=\frac{20}{20} : \frac{60}{20}=1 : 3$
⇒ 1 :3 (b)

Question 6.
The ratio of 150 g to 2 kg is
(a) 75 : 1
(b) 40 : 3
(c) 3 : 40
(d) 3 : 200

We have, 150 g to 2 kg
= 150 g : 2 × 1000 g
= 150 g : 2000 g
Divide both terms by 50
$=\frac{150}{50} : \frac{2000}{50}$
= 3 : 40 (c)

Question 7

In a class of 40 students, 25 students play cricket and the remaining play tennis. The ratio of number of students playing crickets to the number of students playing tennis is
(a) 5 : 8
(b) 5 : 3
(c) 3 : 5
(d) 8 : 5

Total number of students = 40
Student play cricket = 25
Student play tennis = 40 – 25 = 15
Number of students : Number of students
play cricket play tennis
= 25 : 15
Divide both terms by 5
$\frac{25}{5} : \frac{15}{5}$
= 5:3 (b)

Question 8

Two numbers are in the ratio 3 : 5. If the sum of numbers is 144, then the smaller number is
(a) 54
(b) 72
(c) 90
(d) 48

Let any number = x
First number : Second number
3 : 5
Sum of the numbers = 144
⇒ 3x + 5x = 144
⇒ 8x = 144
$x=\frac{144}{8}=18$
First number = 3 × 18 = 54
Second number = 5 × 18 = 90
∴ The smallest number = 54 (a)

Question 9

The ratio of number of girls to the number of boys in a class is 5 : 4. If there are 25 girls in the class, then the number of boys in the class is
(a) 15
(b) 20
(c) 30
(d) 40

Let the number of boys in the class = x
According to question,
Girls : Boys = 5 : 4
25 : x = 5 : 4
$\frac{25}{x}=\frac{5}{4}$
$x=\frac{25 \times 4}{5}=20$
Hence number of boys = 20 (b)

Question 10.

The ratio of the number of sides of a square and the number of edges of a cube is
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 2 : 3

Number of sides of square = 4
Edges of cube = 12
∴ Ratio = 4 : 12
⇒1 : 3 (b)

Question 11.
In shelf, the books with green cover and that with brown cover are in the ratio 2:3. If there are 18 books with green cover, then the number of books with brown cover is
(a) 12
(b) 24
(c) 27
(d) 36

Let the brown covered books = x
and green covered books =18
Green covered books: Brown covered books
= 2 : 3
18 : x = 2 : 3
⇒ $\frac{18}{x}=\frac{2}{3}$
⇒ $x=\frac{18 \times 3}{2}=9 \times 3 \Rightarrow x=27$ (c)

Question 12.

In a box, the ratio of the number of red marbles to that of blue marbles is 4 :7. Which of the following could be the total number of marbles in the box?
(a) 14
(b) 21
(c) 22
(d) 28

The ratio of red marbles to blue marbles = 4:7
⇒ So total marbles can be
4x + 7x = y
11 x=y
y should be a multiple of 11
∴ Total number of marble in the box are 22 (c)

Question 13

If a, b, c and d are in proportion, then
(a) ab = cd
(c) ac = bd
(d) none of these

a, b, c and d are in proportion, then
⇒ $\frac{a}{b}=\frac{c}{d}$

Question 14.
If the weight of 5 bags of rice is 272 kg, then the weight of 1 bag of rice is
(a) 50.4 kg
(b) 54.4 kg
(c) 54.004 kg
(d) 54.04 kg

Weight of 5 bags of rice = 272 kg
Weight of 1 bag of rice = $\frac{272}{5}$ kg
= 54.4 kg (b)

Question 15.
If 7 pencils cost ₹35, then the cost of one dozen pencils is
(a) ₹60
(b) ₹70
(c) ₹30
(d) ₹5

7 pencils cost = ₹35
1 dozen = 12 pencils
Cost of 1 pencil = ₹$\frac{35}{7}$
∴ Cost of 12 pencils (1 dozen) = $\frac{35}{7} \times 12$
= ₹60 (a)

Question 16.
The ratio 2 : 3 expressed as percentage is
(a) 40%
(b) 60%
(c) $66 \frac{2}{3} \%$
(d) $33 \frac{1}{3} \%$

Given, 2 : 3 = $\frac{2}{3}$
$\left(\frac{2}{3} \times 100\right) \%=\frac{200}{3}=66 \frac{2}{3} \%$ (c)

Question 17

0.025 when expressed as percentage is
(a) 250%
(b) 25%
(c) 4%
(d) 2.5%

0.025 =$\frac{25}{1000}$ × 100 = 2.5% (d)

Question 18.
In a class, 45% of the students are girls. If there are 18 girls in the class, then the total number of students in the class is
(a) 44
(b) 40
(c) 36
(d) 30

% of girls in class = 45%
Total number of girls in class = 18
Let total students = x
As per question,
45% of x = 18
$\frac{45}{100} x=18$
$x=\frac{18 \times 100}{45}$
∴Total students = 40 students (b)

#### Value Based Questions, Ratio and Proportion Chapter-8 Class-6 ML Aggarwal Solutions

Question 1

Students of a colony decided to go to an old age home in their vicinity to wish Happy New year and get blessings from old people.
They carried the following items with them:
Bouquets 63, New Year Cards 70 and chocolates bars 140. Answer the following questions:
(i) What is the ratio of number of bouquets to the number of chocolate bars?
(ii) What is the ratio of number of cards to the number of sum of all items?

(i) Number of bouquets = 63
Number of chocolates =140
∴ Ratio of bouquets to number of chocolate bars.
63 : 140 = 9 : 20
(ii) Total number of cards = 70
Sum of all items = 63 + 70 + 140 = 273
∴ Ratio = 70 : 273 = 10: 39

#### HOTS

Question 1

Divide ₹6000 among Irfan, Nagma and Ishan in the raito 3 : 5 : 7.

Total amount = ₹6000
Ratio in Irfan, Nagma and Ishan = 3 : 5 : 7
Sum of ratios = 3 + 5 + 7= 15

Question 2.
Sapna weighs 54 kg on earth and 9 kg on moon. If a monkey weighs 3.5 kg on moon, then how much will it weigh on the earth?

Sapna weight on earth : Sapna weight on moon = Monkey weight on earth : Monkey weight on moon
54 : 9 = x : 3.5

Question 3

If 5 men can do a certain construction work in 14 days, then how long will 7 men take to complete the same construction work?

5 men can do construction on work in = 14 days
1 man can do construction work in = 14 × 5 days
7 men can do construction work in
=$\frac{14 \times 5}{7}$ = 10 days

Question 1

From the given figure, find the ratio of

(i) Number of triangles to the number of circles inside the rectangle.
(ii) Number of squares to the number of all the figures inside the rectangle.
(iii) Number of circles to the number of remaining figures inside the rectangle.

Number of triangles = 3
Number of rectangles = 2
Number of circles = 2
(i) 3 : 2
(ii) 2 : 7
(iii) 2 : 5

Question 2.
The length of a pencil is 16 cm and its diameter is 6 mm. What is the ratio of the diameter of the pencil to that of its length?

Length of a pencil = 16 cm = 16 cm × 10 = 160 mm
Diameter of the pencil = 6 mm
Ratio of the diameter of the pencil to that of its length = 6 : 160 = 3 : 80

Question 3.
A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any game. Find the ratio of number of members who play
(i) badminton to the number of those who play chess.
(ii) badminton to the number of those who do not play any game.
(iii) tennis to the number of those who do not play any game.
(iv) tennis to the number of those who play either badminton or chess.

Total number of members = 100
Members who plays tennis = 25
Members who plays badminton = 28
Members who plays chess = 12
Members who play nothing = 100 – (25 + 28 + 12)
= 35
(i) 28 : 12 = 7 : 3
(ii) 28 : 35 = 4 : 5
(iii) 25 : 28 = 5 : 7
(iv) 25 : 40 = 5 : 8

Question 4.
Do the ratios 15 cm to 3 m and 25 seconds to 3 minutes from a proportion?

Given, first ratio = 15 cm : 3 m
= 15 cm : 300 cm
= 1 : 20
and second ratio = 25 seconds : 3 minutes
= 25 seconds : 3 × 60 seconds
= 25 : 180 = 1 : 6
No, they do not form proportion.

Question 5.
Divide ₹500 among Suresh and Awanti in the ratio 3 : 7.

Total amount = ₹500
Ratio = 3 : 7
Sum of ratios = 3 + 7=10
Suresh shares = ₹$\frac{500 \times 3}{10}$ = ₹150
Awanti shares = ₹ $\frac{500 \times 7}{10}$ = ₹350

Question 6.
The ratio of the number of girls to that of boys in a school is 9 : 11. If the number of boys in the school is 2035, find:
(i) the number of girls in the school,
(ii) the number of students in the school.

Let the number of girls = x
Girls : Boys = 9 : 11
No. of boys = 2035
x : 2035 = 9 : 11

No. of girls = 1665.
(ii) Total students in school = No. of boys + No. of girls
2035 + 1665 = 3700

Question 7.
The ratio of income to expenditure of a family is 7 : 6. Find the savings if the income of family is ₹42000.

Ratio in income and expenditure = 7 : 6
Total income = ₹42000
Let expenditure = x, then
7 : 6 :: 42000 : x
⇒ $x=\frac{6 \times 42000}{7}$ = ₹36000
Now,
Income = ₹42000
Expenditure = ₹36000
∴ Savings = Income – Expenditure
= ₹(42000 – 36000) = ₹6000

Question 8.

An employee earns ₹72,000 in 3 months.
(i) How much does he earn in 7 months?
(ii) In how many months will he earn ₹3,60,000?

(i) ∵ Earning in 3 months = ₹72000
∴ Earning in 1 month = ₹$\frac{72000}{3}$ = 24000
Earning in 7 months = ₹24000 × 7
= ₹1,68,000
(ii) ₹24000 is earned in = 1 month
₹1 is earned is = $\frac{1}{24000}$
₹3,60,000 is earned in

Question 9.

A train travels 110 km in 2 hours and a car travels 245 km in $3 \frac{1}{2}$ hours. What is the ratio of the speed of the train to that of the car?

A train travels in 2 hours =110 km
It will cover in 1 hour = $\frac{110}{2}$ = 55 km
A car travel in $\frac{7}{2}$ hours = 245 km
∴ It will cover in 1 hour =$\frac{2 \times 245}{7}$ = 70 km
Ratios in their speed = 55 : 70 = 11 : 14

-: End of Ratio and Proportion Class-6 ML Aggarwal Solutions  :–