Question

By purchasing $₹25$ shares, for $₹10$ each, a man gets $4\%$ profit on his investment. What rate percent is company paying? What is his dividend, if he buys $80$ shares?

Answer 1

Step 1: Given Data:

Face value$=₹25$

Market value$=₹10$

Profit $\%=4\%$

Number of shares, $N=80$

Step 2: Calculate the dividend given by the company on a share purchased by the man:

$\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{a}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}=\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{\%}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}$

$$\begin{gathered} =\frac{4}{100}\times 10 \\ =₹0.4 \end{gathered}$$

Step 3: Calculate the rate of dividend:

(i) $\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathit{\%}\mathit{}\mathit{=}\mathit{}\frac{\mathit{}\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathit{}\mathit{o}\mathit{n}\mathit{}\mathit{a}\mathit{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}}{\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}}\mathit{\times }\mathit{100}$

$$\begin{gathered} =\frac{0.4}{25}\times 100 \\ =1.6\% \end{gathered}$$

Step 4: Calculate the dividend for 80 shares:

(ii) $\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{80}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}=\mathit{80}\mathbf{\times }\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{a}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}$

$$\begin{gathered} \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}=\mathbf{}80\times 0.4 \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}=\mathbf{}₹\mathbf{}32 \end{gathered}$$

Final Answer:

(i) The rate percent paid by the company is $\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\%}$.

(ii) Dividend received by the man on $80$ shares from the company is $\mathbf{₹}\mathbf{32}$.