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Question
By selling at Rs. 77, some `2(1)/(4)` % shares of face value Rs. 100, and investing the proceeds in 6% shares of face value Rs. 100, selling at 110, a person increased his income by Rs, 117 per annum. How many shares did he sell?
Solution
Let the number of shares = x
On selling at Rs.77, the amt received x × 77 = Rs. 77 x
and dividend received = `77x xx (9)/(4 xx 77) = (9)/(4)x`
Again investing Rs. 77x for the purchase of shares of market value Rs. 110
= `(77x)/(110)` shares
Dividend = `(77x)/(110) xx 6 = (42)/(10)x`
Difference in income
= `(42)/(10)x - (9)/(4)x`
= `(84x - 45x)/(20)`
= `(39)/(20)x`
∴ `(39)/(20)x` = 117
⇒ x = `(117 xx 20)/(39)` = 60
Hence No. of shares sold = 60.
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