Question

John had 1,000 share of a company with a face value of Rs.40 and paying 8% dividend. He sold some of these shares at a discount of 10% and invested the proceeds in Rs.20 shares at a premium of 50% and paying 12% dividend. If the change in his income is Rs.192. find the number of shares sold by him.

Answer 1

Initial income from 1000 shares of value Rs.40 at 8% dividend $=1000\times 40\times \frac{8}{100}=Rs.3200$

Amount for selling x shares at 10% discount $=Rs.36x$ .................(1)

If share value is Rs 20 and purchased with premium 10% ,

number of shares purchased from the amount Rs. 36x, $=\frac{36x}{30}=\frac{6x}{5}$

Income from existing old shares $=(1000-x)\times 40\times \frac{8}{100}=(1000-x)\times \frac{16}{5}$

Income from new shares $=\frac{6x}{5}\times 20\times \frac{12}{100}=\frac{72x}{25}$

Total income = begin mathsize 12px style open parentheses 1000 space minus space x close parentheses 16 over 5 space plus space fraction numerator 72 x over denominator 25 end fraction space equals space 3200 space minus space 192 space equals space 3008 end style

solving the above equation for x, we get $x=600$

Hence number of shares sold is 600