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Question
A man sold some Rs. 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs. 100 shares paying 16% dividend quoted at Rs. 80 and thus increased his income by Rs. 2000. Find the number of shares sold by him.
Solution
Face value of each share = Rs. 100
Market value of each share
= Rs. 100 – Rs.25
= Rs. 75
Rate of dividend = 10%
Let no. of shares = x
Selling price = x × 75 =Rs. 75x
Face value of x share = 100 x
Dividend annually = `100x xx (10)/(100)` = 10x
No. of shares purchased = `(75x)/(80) = (15x)/(16)`
Face value of `(15x)/(16)` shares = `(15)/(16) xx 100 = (1500)/(16)x`
Dividend = `(1500)/(16)x xx (16)/(100)` = 15x
∴ Increase in income = 15x - 10x = 5x
Now 5x = 2000
∴ x = `(2000)/(5)` = 400
∴ No. of shares purchased = 400.
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