A person receives an annual income of ₹ $900$ in buying ₹ $50$ shares selling at ₹ $80$. If the dividend declared is $20 \%$, find the amount invested and the percentage return on investment.
Income $= $ ₹ $900$
Face value (F.V) of each share $= $ ₹ $50$
Market value (M.V) of each share $= $ ₹ $80$
Rat of dividend $= 20 \%$
Let the number of shares bought $= n$
Income $= $ Number of shares $\times$ rate of dividend $\times$ F.V
i.e. $\;$ $900 = n \times \dfrac{20}{100} \times 50$
$\implies$ $n = 90$
i.e. $\;$ Number of shares bought $= n = 90$
$\text{Number of shares} = \dfrac{\text{Sum invested}}{\text{M.V of 1 share}}$
$\therefore \;$ Sum invested $= $ Number of shares $\times$ M.V of 1 share
i.e. Sum invested $= 90 \times 80 =$ ₹ $7200$
$\% \text{ Return on investment} = \dfrac{\text{Income}}{\text{Investment}} \times 100 \%$
i.e. $\;$ $\% \text{ Return on investment} = \dfrac{900}{7200} \times 100 = 12.5 \%$