 QUESTION

# A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10 %. If Rs 1,200 at the end of the year as dividend. Find:$\left( {\text{i}} \right)$ the number of shares he has.$\left( {{\text{ii}}} \right)$ the dividend percent per share.

Hint: Here, we will proceed by firstly finding the market value of one share using the concept that the market value of 1 share is equal to the sum of the face value of one share with the value corresponding to the premium percentage of the face value of one share.

Given, Investment by the man = Rs 8,800
Face value of 1 share = Rs 100
Dividend at the end of the year or Annual dividend = Rs 1,200
$\left( {\text{i}} \right)$ It is also given that the face value is at a premium of 10 % which means the market value of 1 share will be 10 % more than the face value of the share.
i.e., Market value of 1 share = [(Face value of 1 share)+$\dfrac{{10}}{{100}} \times$(Face value of 1 share)]
$\Rightarrow$ Market value of 1 share = 100 + ($\dfrac{{10}}{{100}} \times$100) = 100 + 10 = Rs 110
As, the total investment by the man is done in buying the shares of the company
So, Total number of shares that the man is having = $\dfrac{{{\text{Investment by the man}}}}{{{\text{Market value of 1 share}}}} = \dfrac{{8800}}{{110}} = 80$ shares

Therefore, the total number of shares that the man has bought are 80 shares.

$\left( {{\text{ii}}} \right)$ Also, Dividend percentage per share = $\dfrac{{{\text{Annual dividend}}}}{{{\text{Total number of shares}}}} = \dfrac{{1200}}{{80}} = 15$%.

Therefore, the dividend percent per share is 15 percent.

Note: In this particular problem, the face value of rupees hundred means that the face value of 1 share is equal to Rs 100. It is important to note that the dividend percentage per share for any company can be evaluated by simply dividing the annual dividend or the dividend at the end of the year by the total number of shares that the man is holding.