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Question
By selling at Rs. 92, some 2.5% Rs. 100 shares and investing the proceeds in 5% Rs. 100 shares at Rs. 115, a person increased his annual income by Rs. 90. Find:
(i) the number of shares sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate percent which he earns on his investment.
Solution
Rate of dividend = 2.5% and market price = Rs. 92
Let number of shares purchased = x.
Selling price of x shares = 92 x
Income from investing
₹ x = `(92x xx 2.5)/(92)`
= `(92 xx x 25)/(92 xx 10)`
= `(5)/(2)x`
Again by investing 92 x in 5% at ₹ 115
the dividend = `(92x xx 5)/(115)` = 4x
Difference = `4x - (5)/(2)x = (3)/(2)x`
∴ `(3)/(2)x` = 90
⇒ x = `(90 xx 2)/(3)` = 60
(i) ∴ No. of shares = 60
(ii) No. of shares sold = `(92x)/(115)`
= `(92 xx 60)/(115)` = 48
(iii) New income = 4x = 4 x 60 = ₹ 240
(iv) Rate percent interest on investment
= `(5 xx 100)/(115)`
= `(100)/(23)`
= `4(8)/(23)`%.
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