**Exercise 9.3**

**1. Which of the following are in proportion?**

**(i) 33, 44, 66, 88**

**Solution:**

We have,

∴ 33 : 44 = 66: 88

Thus, 33: 44, 66, 88 are in pro proportion

**(ii) 46, 69, 69, 46**

**Solution:**

We have:

∴ 46: 69 ≠ 69: 46

Thus, 46, 69, 69, 46 are not in proportion.

**(iii) 72, 84, 186, 217**

**Solution:**

We have,

72, 84, 184, 217

Thus, 72, 84, 186, 217 are in proportion.

**2. Find x in the following proportions**

** (i) 16:1= x:96**

**Solution:**

**(ii) x:92 = 87 : 116**

**Solution:**

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

**Solution:**

The ratio of income and expenditure = 7: 6

7x = 1400

x = 200

Expenditure = 6x = 6 × 200

= Rs.1200

Savings = Income – Expenditure

= 1400 -1200

= Rs.200

**4. 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?**

**Solution:**

The scale of map = 1: 4000000

Let us assume the actual distance between towns is x cm

1: 4000000 =5: x

x = 5 × 4000000

= 20000000 cm

1km = 1000 m

1m = 100 cm

Therefore, x = 200 km

**5. 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?**

**Solution:**

Given that the ratio of income of a person to his savings is 10:1

Savings per year = 6000

Savings per month = 6000/12

= Rs. 500

Than let income per month be x

X: 5000 = 10: 1

X = 500×10

X = 5000

Income per month is Rs. 5000

**6. 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.**

**Solution:**

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 = 120/8

x = 15