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 share sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate per cent which he earns on his investment.

Answer 1

Step 1: Given information

The market value of a share$=\mathrm{Rs}.92$

Rate of dividend$=2.5\%$

Step 2: Calculate the number of shares

Let us consider the number of shares purchased is $x$.

The selling price of x shares$=\mathrm{Rs}.92x$

Income from investing $\mathrm{Rs}.92x$ at $2.5\%$ of $\mathrm{Rs}.92$ is computed as:

$\begin{array}{rcl}& \Rightarrow & \mathrm{Income}=\frac{92x\times 2.5}{92}\\ \therefore \mathrm{Income}& =& \mathrm{Rs}.2.5x\end{array}$

Again by investing $\mathrm{Rs}.92x$in $5\%$ at $\mathrm{Rs}.115$:

Income from investing is computed as;

$$\begin{gathered} \mathrm{Income}=\frac{92x\times 5}{115} \\ \mathrm{Income}=\mathrm{Rs}.4x \end{gathered}$$

Since, after investing in $5\%\mathrm{Rs}.100$ shares at$\mathrm{Rs}.115$, a person increased his annual income by $\mathrm{Rs}.90$

$\begin{array}{rcl}\mathrm{Difference}& =& 4\mathrm{x}-2.5\mathrm{x}=1.5\mathrm{x}\\ & \Rightarrow & \mathrm{Difference}=\text{Rs}.90\end{array}$

$\begin{array}{rcl}& \Rightarrow & 1.5x=90\end{array}$

$\begin{array}{rcl}& \Rightarrow & x=\frac{90}{1.5}\end{array}$

$\begin{array}{rcl}& \Rightarrow & x=60\end{array}$

The number of shares$=60$

Thus, the number of shares sold is $60$.

Step 3 : Calculate the number of shares purchased

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{share}\mathrm{purchased}& =& \frac{92}{115}x\\ & =& \frac{92}{115}\times 60\\ & =& 48\end{array}$

Step 4: Calculate new income

$\begin{array}{rcl}\mathrm{New}\mathrm{income}& =& 4x\\ & =& 4\times 60\\ & =& \mathrm{Rs}.240\end{array}$

Step 5: Calculate rate percent

Rate percent is computed as:

$\begin{array}{rcl}\mathrm{Rate}& =& \frac{5\times 100}{115}\\ & =& \frac{100}{23}\\ \therefore \mathrm{Rate}& =& 4\frac{8}{23}\%\end{array}$

Hence,

(i) The number of shares sold is $60$.

(ii) The number of shares purchased is $48$.

(iii) The new income is $\mathrm{Rs}.240$.

(iv) The rate percent is $4\frac{8}{23}\%$.