RD Sharma Solutions Class 7 Ratio And Proportion Exercise 9.3

RD Sharma Solutions Class 7 Chapter 9 Exercise 9.3

RD Sharma Class 7 Solutions Chapter 9 Ex 9.3 PDF Free Download

Exercise 9.3

Q1. Which of the following are in proportion?

(i) 33,44,66,88

We have,

\(33:44=\frac{3}{4}\;\;\;and\;\;\;66:88=\frac{3}{4}\\ Therefore\;33:44=66:88\)

Hence 33,44,66,88 are in proportion

(ii) 46,69,69,46         

We have,

\(46:69=\frac{2}{3}\;\;\;and\;\;\;69:46=\frac{3}{2}\\\)

Hence 46,69,69,46 are not in proportion

(iii) 72,84,186,217

We have,

\(72:84=\frac{6}{7}\;\;\;and\;\;\;186:217=\frac{6}{7}\\ Therefore\;72:84=186:217\)

Hence 72,84,186,217 are in proportion

 Q2. Find x in the following proportions

(i) 16:18=x:96

\(\frac{16}{18}=\frac{x}{96}\\ x=\frac{256}{3}\)

(ii) x:92=87:116

\(\frac{x}{92}=\frac{87}{116}\\ x=\frac{87\times92}{116}\\ x=69\)

 

Q3. The ratio of income to the expenditure of a family is 7:6. Find the savings if the income is Rs.1400.

The ratio of income and expenditure=7:6

7x=1400

x=200

Expenditure=6x=\(6\times200\)=Rs.1200

Savings= Income-Expenditure

=1400-1200

=Rs.200

 

Q4. The scale of a map is 1:4000000. What is the actual distance between the two towns if they are 5cm apart on the map?

The scale of map=1:4000000

Let us assume the actual distance between towns is x cm

1:4000000=5:x

x=\(5\times4000000\)=20000000cm

1km=1000m

1m=100cm

Therefore

x=200km

 

Q5. The ratio of income of a person to his savings is 10:1. If his savings for one year is Rs.6000, what is his income per month?

The ratio of income of a person to his savings is 10:1

Savings per month=\(\frac{6000}{12}\)

=Rs.500

Then let income per month be x

x:500=10:1

x=\(500\times10\)

x=5000

Q6. An electric pole casts a shadow of length 20 metres at a time when a tree 6 metres high casts a shadow of length 8 metres. Find the height of the pole

Height of the tree: Length of the shadow of tree

Height of the pole: Length of the shadow of pole

x:20=6:8

\(x=\frac{120}{8}\)

x=15