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

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

Answer

Investments are as follows :
(1) Total : Rs. 12,000 (2) Bank : Rs. 3000 (3) More in immovable property then MF : Rs. 2000
(4) Post : Rs. 1000 .

Explanation

(1) Let the total investment be Rs. 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^(@)`
` :. 60^(@) = (2000)/x xx 360^(@)`
` :. x = (2000 xx 360)/ 60`
` :. x = 12000` ...(1)
` :. ` total investment is Rs . 12,000.
(2) Let the amount deposited in the bank be Rs. y.
The central angle for the amount deposited in the bank
` = "the amount deposited in the bank "/"total investement" xx 360^(@)`
` :. 90^(@) = y/(12000) x 360^(@) ` ... (The central angle for the amount deposited in bank is given to be `90^(@)`)
` :. y = (90 xx 12000)/360`
` :. y = 3000` ...(2)
(3) Let the amount invested in the mutual fund be Rs. z .
The central angle for the amount invested in the mutual fund is `60^(@)`.
The central angle for mutual fund
` = " the amount invested in the mutual fund "/"total investment" xx 360^(@)`
` :. 60^(@) = z/(12000) xx 360^(@) " " :. z = (60 xx 12000)/(360) `
` :. z = 2000` ....(3A)
Now, we find the money invested in the immovable property. Let it be Rs. p.
The central angle for the immovable property
` = "the amount invested in immovable property "/"total investment" xx 360^(@)`
` :. 120^(@) = p/12000 xx 360^(@)`
` :. p = (120 xx 12000)/360`
` :. p = 4000` ...(3B)
More money invested in the immovable property
= Rs. `(400-2000)` ...[From (3B) and (3A)]
= Rs. 2000
(4) The amount invested in the post
= Total investment - (Investment in : MF + immovable property + bank + shares)
` = Rs. [12000 - (2000 + 4000 + 3000 + 2000)]`
` = Rs. (12000 - 11000) = Rs. 1000` ....(4)