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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?
Solution
Measure of central angle (θ) = `"Number of scores in the components"/"Total number of scores" × 360°`
(1) Central angle for shares (θ) = 60°
∴ 60° = `"Amount invested in shares"/"Total investment" × 360°`
∴ 60° = `2000/"Total investment" × 360°`
∴ Total investment = `(2000 × 360°)/(60°) = ₹ 12000`
The total investment is Rs. 12000.
(2) Central angle for deposit in bank (θ) = 90°
∴ 90° = `"Amount deposited in bank"/"Total investment" × 360°`
∴ 90° = `"Amount deposited in bank"/12000 × 360°`
∴ Amount deposited in bank = `(90° × 12000)/(360°) = ₹ 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" × 360°`
∴ Difference in investments = `(60° × 12000)/(360°)` = ₹ 2000
∴ Rs. 2000 more is invested in immovable property than in mutual fund.
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