Question

A man buys \[200\] ten-rupee shares at \[Rs12.50\] each and receives a dividend of $ 8\% $ . Find the amount invested by him and the dividend received by him in cash.

Answer 1

Hint: We can solve the given question by Investment and Dividend formula, and a man buys \[200\]ten rupees shares which means $ 200 \times 10 $ .

Complete step by step answer:
We will find this problem using Investment $ = n \times M.V $ of one share where n is the number of the shares and M.V is the market value (at which one share is sold) of the given problem and Dividend formula is
Dividend = $ n \times \dfrac{r}{{100}} \times N.V $ of the one share where, r is the rate and N.V is the Nominal value of the shares.
Since from given a man buys a total number of shares(n) $ = 200 $ , which are ten rupees share, so the nominal value of one share (N.M) $ = R.s.10 $
Therefore, face value of $ 200 $ shares $ = 10 \times 200 $
 $ \Rightarrow Rs.2000 $
Now the amount invested for the purchase of $ 200 $ shares at the rate of $ Rs.12.50 $ each is $ \Rightarrow 12.50 \times 200 $
Multiplying the above equation, we get $ \Rightarrow Rs.2500 $ (By investment formula)
Since from given the rate of the dividend is $ 8\% $
Thus Dividend = $ n \times \dfrac{r}{{100}} \times N.V $ = $ 200 \times (\dfrac{8}{{100}}) \times 10 $
Solving this equation, we get Dividend $ = 2 \times 8 \times 10 = 160 $
Hence the amount invested by him is $ Rs.2500 $ and the dividend received by him is $ Rs.160 $

Note: We must make an error on the dividend formula like $ n \times \dfrac{{r\% }}{{100}} \times N.V $
But here the % (percentage) already represents the $ \dfrac{1}{{100}} $ so we don’t need to repeat it again.
The market value of one share (M.V) = the price at which the shares are brought – total nominal value
Hence, we can also use this formula to find one share which is $ 212.50 - 200 = 12.50.Rs $ ( $ Rs.212.50 $ is the man who buys ten rupees shares at the price).