Question

A man buys $200$ ten-rupees shares at $212.50$ each and receives a dividend of $8$ %. Find the amount invested by him and the dividend received by him in cash.

Answer 1

Hint: You can solve the question using the formula, ${\text{Investment = n}} \times {\text{M}}{\text{.V}}{\text{.of one share}}$ where n is the number of the shares and M.V. is the market value (at which one share is sold) of share. You can find dividend by using formula, ${\text{Dividend = n}} \times \dfrac{{\text{r}}}{{100}} \times {\text{N}}{\text{.V}}{\text{. of one share}}$ where r is the rate and N.V. is the nominal value of the shares.

Complete step-by-step answer:
Given, a man buys a total number of shares (n) =$200$, which are ten rupees shares. So the nominal value of one share (N.V.) =${\text{Rs}}.10$.Since the man buys ten rupees shares at the price of $212.50$then,
The market value of one share= the price at which the shares are bought - total nominal value
The market value of one share(M.V.) =$212.50 - 200 = 12.50$ Rs.
He receives the dividend of rate r=$8$ %. We have to find the amount of investment and the dividend received by him . For finding the investment, we will use the formula
$ \Rightarrow $ ${\text{Investment = n}} \times {\text{M}}{\text{.V}}{\text{.of one share}}$ Where n is the number of the shares and M.V. is the market value
On putting the given values in the formula and simplifying, we get-
$ \Rightarrow $ Investment $ = 200 \times 12.50 = 2500$
For the dividend we use the formula,
$ \Rightarrow {\text{Dividend = n}} \times \dfrac{{\text{r}}}{{100}} \times {\text{N}}{\text{.V}}{\text{. of one share}}$
On putting the given values in the formula and simplifying, we get-
$ \Rightarrow $ Dividend$ = 200 \times \left( {\dfrac{8}{{100}}} \right) \times 10 = 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: Many students write the dividend formula as- ${\text{Dividend = n}} \times \dfrac{{{\text{r% }}}}{{100}} \times {\text{N}}{\text{.V}}{\text{. of one share}}$ which is wrong as $% $ means$\dfrac{1}{{100}}$ so either write the $% $sign or write$\dfrac{1}{{100}}$. The correct formula will be-
$ \Rightarrow {\text{Dividend = n}} \times {\text{r% }} \times {\text{N}}{\text{.V}}{\text{. of one share}}$ Which when simplified is written as-
$ \Rightarrow {\text{Dividend = n}} \times \dfrac{{\text{r}}}{{100}} \times {\text{N}}{\text{.V}}{\text{. of one share}}$