A person invests ₹ $9900$ on buying shares of face value of ₹ $100$ each at a premium of $10 \%$ in a company. If the person earns ₹ $1350$ at the end of the year, find
- the number of shares the person has in the company and
- the dividend percent per share.
Amount invested $= $ ₹ $9900$
Face value (F.V) of each share $= $ ₹ $100$
Market value (M.V) of each share $= $ ₹ $\left(100 + \dfrac{10}{100} \times 100\right) = $ ₹ $110$
$\text{Number of shares bought} = \dfrac{\text{Amount invested}}{\text{M.V of each share}} = \dfrac{9900}{110} = 90$
Let dividend percent per share $= d \%$
Dividend on $1$ share $= d \% \text{ of F.V} = d \% \text{ of }$ ₹ $100 = $ ₹ $d$
$\therefore \;$ Income from $90$ shares $= $ ₹ $90 d$
Given: Annual income $= $ ₹ $1350$
i.e. $\;$ $90 d = 1350$ $\implies$ $d = 15$
$\therefore \;$ Dividend percent per share $= 15 \%$