Std 6 Mathematics · Chapter 7

7. Ratio and Proportion

Solutions to Practice Set 7.1, Practice Set 7.2 and Exercise 7. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

A ratio compares two quantities of the same kind. In this chapter, we learn to write a ratio in its simplest form. We find the ratio of quantities with different units. We also learn the unitary method. In this method, we first find the value of one thing.

Key points

The ratio of a to b is written as a : b. It is read as "a is to b".
A ratio can also be written as a fraction, like 5 : 7 = 5/7.
To write a ratio in simplest form, divide both terms by their GCD.
Before finding a ratio, write both quantities in the same unit.
A ratio has no unit. The order of the terms is important.

Formulas and terms

Terms of a ratio – in 3 : 5, 3 is the first term and 5 is the second term.
Simplest form – a ratio whose terms have no common divisor except 1.
Unitary method – find the value of one by division. Then find the required value by multiplication.
1 kg = 1000 g, 1 l = 1000 ml, 1 m = 100 cm, 1 hour = 60 minutes, 1 year = 12 months

Practice Set 7.1

1Write the ratio of the first number to the second number in its simplest form.

(i) 36 : 88 = 36/88 = 36 ÷ 4/88 ÷ 4 = 9/22 = 9 : 22
(ii) 72 : 18 = 72/18 = 72 ÷ 18/18 ÷ 18 = 4/1 = 4 : 1
(iii) 91 : 65 = 91/65 = 91 ÷ 13/65 ÷ 13 = 7/5 = 7 : 5
(iv) 85 : 102 = 85/102 = 85 ÷ 17/102 ÷ 17 = 5/6 = 5 : 6

2Write the ratio of the second number to the first number in its simplest form.

(i) 28, 84 → 84 : 28 = 84 ÷ 28/28 ÷ 28 = 3 : 1
(ii) 120, 32 → 32 : 120 = 32 ÷ 8/120 ÷ 8 = 4 : 15
(iii) 75, 135 → 135 : 75 = 135 ÷ 15/75 ÷ 15 = 9 : 5
(iv) 220, 100 → 100 : 220 = 100 ÷ 20/220 ÷ 20 = 5 : 11

Here the second number is written first.

3Find the ratio of the first quantity to the second quantity in its simplest form.

(i) 5 years, 10 months

5 years = 5 × 12 = 60 months
60 : 10 = 6 : 1

(ii) 750 grams, 1.5 kg

1.5 kg = 1500 g
750 : 1500 = 1 : 2

(iii) 5 l, 500 ml

5 l = 5000 ml
5000 : 500 = 10 : 1

(iv) 135 minutes, 2 hours

2 hours = 120 minutes
135 : 120 = 9 : 8

(v) 2.1 m, 70 cm

2.1 m = 210 cm
210 : 70 = 3 : 1

4320 workers are working in a factory, of whom 200 are male workers. Find the ratios: a) male to female workers b) male to total workers c) female to total workers.

Total workers = 320
Male workers = 200
Female workers = 320 − 200 = 120

a) Male : female = 200 : 120 = 5 : 3
b) Male : total = 200 : 320 = 5 : 8
c) Female : total = 120 : 320 = 3 : 8

Practice Set 7.2 – Unitary Method

1A charitable organization wants to gift one compass box each to 67 needy students. A pack of 10 compass boxes costs ₹850. How much will the organization spend?

Cost of 10 compass boxes = ₹850
Cost of 1 compass box = 850 ÷ 10 = ₹85
Cost of 67 compass boxes = 67 × 85 = ₹5695

The organization will spend ₹5695.

2A goods train covers 240 km at a constant speed in 4 hours. How much distance will it cover in 7 hours?

Distance covered in 4 hours = 240 km
Distance covered in 1 hour = 240 ÷ 4 = 60 km
Distance covered in 7 hours = 7 × 60 = 420 km

The goods train will cover 420 km in 7 hours.

Exercise 7

1Choose the correct option.

(i) Which fraction shows the ratio 5 : 7? — a) 5/7
The ratio 5 : 7 is written as the fraction 5/7.
(ii) What is the simplest form of 60/36? — d) 5/3
The GCD of 60 and 36 is 12. 60 ÷ 12 = 5 and 36 ÷ 12 = 3.
(iii) What is the ratio of 2 kg to 800 grams? — c) 5/2
2 kg = 2000 g. So, 2000 : 800 = 5 : 2.

2In a class of 45 students, 15 play hockey, 20 play kabaddi and the rest play kho-kho. Each student plays only one game. Find the ratios: (i) hockey players to kho-kho players (ii) kabaddi players to total students (iii) hockey players to total students.

Students who play kho-kho = 45 − (15 + 20) = 45 − 35 = 10

(i) Hockey : kho-kho = 15 : 10 = 3 : 2
(ii) Kabaddi : total = 20 : 45 = 4 : 9
(iii) Hockey : total = 15 : 45 = 1 : 3

3Colour any three squares in the figure of 10 squares. Find the ratios: (i) coloured squares to total squares (ii) uncoloured squares to total squares (iii) coloured squares to uncoloured squares.

Ten squares with any three of them coloured.

Total squares = 10
Coloured squares = 3
Uncoloured squares = 10 − 3 = 7

(i) Coloured : total = 3 : 10
(ii) Uncoloured : total = 7 : 10
(iii) Coloured : uncoloured = 3 : 7

4The length of a rectangular sheet is 1.20 m and the width is 48 cm. Find the ratio of the width to the length.

Length = 1.20 m = 1.20 × 100 = 120 cm
Width : length = 48 : 120
= 48 ÷ 24/120 ÷ 24 = 2/5 = 2 : 5

The ratio of the width to the length is 2 : 5.

5Michael's monthly income is ₹52,000, of which he saves ₹13,000. Find the ratio of his income to his expenditure.

Expenditure = Income − Savings
= 52,000 − 13,000 = ₹39,000
Income : Expenditure = 52,000 : 39,000
= 52000 ÷ 13000/39000 ÷ 13000 = 4/3 = 4 : 3

The ratio of his income to his expenditure is 4 : 3.

6A school bought 35 saplings from 'Yashoda' nursery for ₹455 and the remaining saplings of the 50 needed from 'Amol' nursery for ₹240. From which nursery are the saplings cheaper?

Yashoda nursery
Cost of 35 saplings = ₹455
Cost of 1 sapling = 455 ÷ 35 = ₹13

Amol nursery
Saplings bought = 50 − 35 = 15
Cost of 15 saplings = ₹240
Cost of 1 sapling = 240 ÷ 15 = ₹16

₹13 is less than ₹16. So, the saplings are cheaper at 'Yashoda' nursery.

7A cook prepares 10 kg of rice every day for 100 students. One day only 80 students were present. How much rice should be cooked that day?

Rice for 100 students = 10 kg
Rice for 1 student = 10 ÷ 100 = 1/10 kg = 100 g
Rice for 80 students = 80 × 1/10 = 8 kg

8 kg of rice should be cooked that day.

✦Do it – measure the length of your full arm and your hand-span, and find the ratio.

This is an activity. Measure both lengths in centimetres. For example:

Length of the arm = 60 cm
Length of the hand-span = 20 cm
Ratio = 60 : 20 = 3 : 1

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