Question

By selling at $Rs.77$, some $2\frac{1}{4}\%$ shares of face value $Rs.100$, and investing the proceeds in $6\%$ shares of face value of $Rs.100$, a person increased his income by $Rs.117$ per annum. How many shares did he sell?

Answer 1

Let $x$ be the shares a person sold for $Rs.77$ and it has a face value of $Rs.100$.

And income per annum on these shares is $2\frac{1}{4}\%=\frac{9}{4}\times 100$

$=Rs.\frac{9x}{4}$

So, the selling price of the shares will be $Rs.77x$

The purchase price of each share is $Rs.110$ and the face value is $Rs.100$

And the number of shares the person purchased by selling the previous shares:

$\frac{77x}{110}=\frac{7x}{10}$

The income on each share per annum is $6\%$ of $Rs.100=Rs.6$

The income on $\frac{7x}{10}$ shares $=Rs.6\times \frac{7x}{10}$

$=Rs.\frac{21x}{5}$

So, the income is increasing by $117$ per annum

$\frac{21x}{5}-\frac{9x}{4}=117$

$\frac{84x-45x}{20}=117$

$\frac{39x}{20}=117$

$x=20\times \frac{117}{39}$

$x=60$

therefore person has sold $60$ shares

Hence, this is the answer.