Question

The annual investments of a family are shown in the adjacent pie diagram. Answer the following questions based on it.

1. If the investment in shares is ₹ 2000, find the total investment.
2. How much amount is deposited in the bank?
3. How much more money is invested in immovable property than in mutual fund?
4. How much amount is invested in post?

The annual investments of a family are shown in the following pie diagram. Answer the following questions based on it.

1. If the investment in the shares is ₹ 2000, find the total investment.
2. How much amount is deposited in the Post?

Answer 1

Measure of central angle (θ) = `"Number of scores in the components"/"Total number of scores" xx 360^\circ`

(1) Central angle for shares (θ) = 60°

∴ 60° = `"Amount invested in shares"/"Total investment" xx 360^\circ`

∴ 60° = `2000/"Total investment" xx 360^\circ`

∴ Total investment = `(2000 xx 360^\circ)/(60^\circ)` = ₹ 12000

The total investment is Rs. 12000.

(2) Central angle for deposit in bank (θ) = 90°

∴ 90° = `"Amount deposited in bank"/"Total investment" xx 360^\circ`

∴ 90° = `"Amount deposited in bank"/12000 xx 360^\circ`

∴ Amount deposited in bank = `(90^\circ xx 12000)/(360^\circ)` = ₹ 3000

∴ The amount deposited in bank is Rs. 3000.

(3) Difference in central angle for immovable property and mutual fund (θ) = 120° – 60° = 60°

∴ 60° = `"Difference in investments"/"12000" xx 360^\circ`

∴ Difference in investments = `(60^\circ xx 12000)/(360^\circ)` = ₹ 2000

∴ Rs. 2000 more is invested in immovable property than in mutual fund.

(4) Central angle for post (θ) = 30°

∴ 30° = `"Amount deposited in post"/12000 xx 360^\circ`

∴ Amount invested in post = `(30^\circ xx 12000)/(360^\circ)` = ₹ 1000

∴ The amount invested in post is Rs. 1000.

Answer 2

a. Let the total investment be ₹ x.

The central angle for the investment in shares is given to be 60°.

The central angle for the investment in shares

= `"investment in shares"/"total investment" xx 360^\circ`

= 60° = `2000/x xx 360^\circ`

∴ x = `(2000 xx 360^\circ)/60^\circ`

∴ x = 12000

∴ the total investment is ₹ 12,000.

b. Let the amount deposited in post be ₹ y.

The central angle for the amount deposited in post

= `"the amount deposited in post"/"total investment" xx 360^\circ`

∴ 30° = `y/12000 xx 360^\circ`

∴ y = `(30^\circ xx 12000)/360^\circ`

= `12000/12`

∴ y = 1000