Exercise 6.2

1. Find the missing numbers in the following proportions in the table given below.

2. Write true or false.

3. Madhu buys 5 kg of potatoes at the market. If the cost of 2 kg is ₹36, how much will Madhu pay?

Solution:

Given:

Cost of kg potatoes = ₹

Let's set up the proportion:

2 kg : ₹36 :: 5 kg : x

Using cross multiplication:

2x = 36 ×

x = (36 × 5) ÷ 2

x =

Therefore, Madhu will pay ₹90 for 5 kg of potatoes.

4. A man whose weight is 90 kgs weighs 15 kg on the moon, what will be the weight of a man whose weight is 60 kg?

Solution:

Given:

Earth weight : Moon weight

kg : kg

Let's set up the proportion:

90 : 15 :: 60 : x

Using cross multiplication:

90x = 15 ×

x = (15 × 60) ÷ 90

x =

Therefore, a 60 kg man will weigh 10 kg on the moon.

5. A disaster relief team consists of engineers and doctors in the ratio of 2 : 5.

Solution:

(i) If there are 18 engineers, find the number of doctors:

Given ratio = 2 :

Number of engineers =

Let's find the number of doctors:

2 parts = 18 engineers

1 part = engineers

Therefore:

5 parts = 5 × 9 = doctors

(ii) If there are 65 doctors, find the number of engineers:

Given:

5 parts = doctors

1 part = doctors

Therefore:

2 parts = 2 × 13 = engineers

6. The ratio of two angles is 3 : 1. Find the:

Solution:

(i) Larger angle if the smaller is 180°:

Given:

Ratio = :

Smaller angle = °

Therefore:

If 1 part = 180°

3 parts = 3 × 180° = °

(ii) Smaller angle if the larger is 63°:

Given:

Ratio = 3 : 1

Larger angle (3 parts) = °

Therefore:

3 parts = 63°

1 part = 63° ÷ 3 = °