R d sharma mathematics solutions class 6 Solutions for Chapter 9 ratio proportion and unitary method

Express each of the following in the language of ratios:

(i) In a class, the number of girls in the merit list of the board examination is two times that of boys.

(ii) The number of students passing mathematics test is 2/3 of the number that appeared.

Express the following ratios in language of daily life:

(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9.

(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1.

Express each of the following ratios in its simplest form:

(i) 60: 72

(ii) 324: 144

(iii) 85: 391

(iv) 186: 403

Find the ratio of the following in the simplest form:

(i) 75 paise to Rs 3

(ii) 35 minutes to 45 minutes

(iii) 8 kg to 400 gm

(iv) 48 minutes to 1 hour

(v) 2 metres to 35 cm

(vi) 35 minutes to 45 seconds

(vii) 2 dozen to 3 scores

(viii) 3 weeks to 3 days

(ix) 48 min to 2 hours 40 min

(x) 3 m 5 cm to 35 cm

Find the ratio of

(i) 3.2 metres to 56 metres

(ii) 10 metres to 25 cm

(iii) 25 paise to Rs 60

(iv) 10 litres to 0.25 litre

The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number of boys to that of the girls in the simplest form

Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000per month. Find the following ratios:

(i) Avinash’s income to the income of his wife.

(ii) Avinash’s income to their total income.

Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio ofthe number of:

(i) men to that of women,

(ii) men to the total number of persons

(iii) persons to that of women.

The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is theratio of its length to width?

An office opens at 9 am and closes at 5 pm with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?

A bullock-cart travels 24 km in 3 hours and a train travels 120 km in 2 hours. Find the ratio of their speeds.

Margarette works in a factory and earns Rs 955 per month. She saves Rs 185 per month from her earnings. Find the ratio of:

(i) her savings to her income

(ii) her income to her expenditure

(iii) her savings to her expenditure.

Which ratio is larger in the following pairs?

(i) 3: 4 or 9: 16

(ii) 15: 16 or 24: 25

(iii) 4: 7 or 5: 8

(iv) 9: 20 or 8: 13

(v) 1: 2 or 13: 27

Give two equivalent ratios of 6: 8.

Fill in the following blanks:

12/20 = ☐/5 = 9/☐

Which of the following statements are true?

(i) 16: 24 = 20: 30

(ii) 21: 6 = 35: 10

(iii) 12: 18 = 28: 12

(iv) 51: 58 = 85: 102

(v) 40 men: 200 men = Rs 5: Rs 25

(vi) 99 kg: 45 kg = Rs 44: Rs 20

Find which of the following are in proportion:

(i) 8, 16, 6, 12

(ii) 6, 2, 4, 3

(iii) 150, 250, 200, 300

Find x in the following proportions:

(i) x: 6 = 55: 11

(ii) 18: x = 27: 3

(iii) 7: 14 = 15: x

(iv) 16: 18 = x: 96

Set up all proportions from the numbers 9, 150, 105, 1750.

Find the other three proportions involving terms of each of the following:

(i) 45: 30 = 24: 16

(ii) 12: 18 = 14: 21

If 4, x, 9 are in continued proportion, find the value of x.

If in a proportion, the first, second and fourth terms are 32, 112 and 217 respectively, find the third term.

Show that the following numbers are in continued proportion:

(i) 36, 90, 225

(ii) 48, 60, 75

(iii) 16, 84, 441

The ratio of the length of a school ground to its width is 5: 2. Find its length if the width is 40metres.

The ratio of the sale of eggs on a Sunday to that of the whole week of a grocery shop was 2: 9. Ifthe total sale of eggs in the same week was Rs 360, find the sale of eggs onSunday.

The ratio of copper and zinc in an alloy is 9: 7. If the weight of zinc in the alloy is 9.8 kg, find theweight of copper in the alloy.

The ratio of the income to the expenditure of a family is 7: 6. Find the savings if the income is Rs 1400

The ratio of story books in a library to other books is 1: 7. The total number of story books is 800.Find the total number of books in the library.

The price of 3 metres of cloth is Rs 79.50. Find the price of 15 metres of such cloth.

The cost of 17 chairs is Rs 9605. Find the number of chairs that can be purchased in Rs 56500.

Three ferryloads are needed to carry 150 people across a river. How many people will be carried on 4 ferryloads?

If 9 kg of rice costs Rs 120.60, what will 50 kg of such a quality of rice cost?

A train runs 200 kilometres in 5 hours. How many kilometres does it run in 7 hours?

10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?

A man can work 8 hours daily and finishes a work in 12 days. If he works 6 hours daily, in how many days will the same work be finished?

Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? How many postcards can bebuy in Rs 45?

A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?

If the sales tax on a purchase worth Rs 60 is Rs 4.20. What will be the sales tax on the purchaseworth Rs 150?

The cost of 17 chairs is Rs 19210. Find the number of such chairs that can be purchased in Rs 113000?

A car travels 165 km in 3 hours

(i) How long will it take to travel 440 km?

(ii) How far will it travel in 7 hours?

2 dozens of oranges cost Rs 60. Find the cost of 120 similar oranges?

A family of 4 members consumes 6 kg of sugar in a month. What will be the monthly consumption of sugar, if the number of family members becomes 6?

The weight of 45 folding chairs is 18 kg. How many such chairs can be loaded on a truck havinga capacity of carrying 4000 kg load?