Question

Ram invested $₹54000$ in $18\%$, $₹200$ shares of Jindal Electronics. He bought them at a rate such that the percentage return on his investment is $16\%$. Later he sold them, when the market price was $₹275$ and invested the proceeds in buying $24\%$, $₹100$ shares of Golmal Entertainment. If his annual income increased by $₹1920$, then the rate, at which he bought the Golmal Entertainment shares is

• A. $₹120$
• B. $₹180$
• C. $₹150$
• D. $₹160$

Answer 1

The correct option is C

$₹150$

Step 1: Given Data

Investment in Jindal Electronics's share made by Ram, $I_1=₹54000$

Face value of Jindal Electronics's share, $F_1=₹200$

Dividend of Jindal Electronics's share, $D_1=18\%$

Return% of Jindal Electronics's share, $R_1=16\%$

Selling price of one share of Jindal Electronics, $SP=₹275$

Face value of Golmal Entertainment's shares, $F_2=₹100$

Dividend of Golmal Entertainment's shares, $D_2=24\%$

Increase in Ram's annual income$=₹1920$

Step 2: Calculate the number of Jindal Electronics's shares

Let us assume that the market value of Jindal Electronics's share be $M_1$. Using the formula,

$\mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathbf{\%}\mathbf{\times }\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}=\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathbf{\%}\mathbf{\times }\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}$

$$\begin{gathered} R_1\times M_1=D_1\times F_1 \\ 16\times M_1=18\times 200 \\ {M}_1=\frac{18\times 200}{16} \\ {M}_1=₹225 \end{gathered}$$

Now, $\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}=\frac{\mathit{I}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}{\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}}$

$$\begin{gathered} N_1=\frac{I_1}{M_{\mathit{1}}} \\ =\frac{54000}{225} \\ =240\mathrm{shares} \end{gathered}$$

Step 3: Calculate the sale proceeds of Ram on Jindal Electronics's shares sold

$\mathit{S}\mathit{a}\mathit{l}\mathit{e}\mathbf{}\mathit{p}\mathit{r}\mathit{o}\mathit{c}\mathit{e}\mathit{e}\mathit{d}\mathit{s}=\mathbf{}\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{\times }\mathit{S}\mathit{e}\mathit{l}\mathit{l}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{o}\mathit{n}\mathit{e}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}$

$$\begin{gathered} =240\times 275 \\ =₹66000 \end{gathered}$$

Step 4: Calculate the annual income of Ram on Jindal Electronics's shares

$\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathit{i}\mathit{n}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathbf{}=\mathbf{}\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{\times }\mathit{N}\mathit{o}\mathit{m}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\frac{\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}}{\mathit{100}}$

$$\begin{gathered} A_1=N_1\times F_1\times \frac{D_1}{100} \\ =240\times 200\times \frac{18}{100} \\ =₹8640 \end{gathered}$$

Step 5: Calculate the annual income of Ram on Golmal Entertainment's shares

Let us assume that the number of shares bought be $y$.

$\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathit{i}\mathit{n}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathbf{}=\mathbf{}\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{\times }\mathit{N}\mathit{o}\mathit{m}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\frac{\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}}{\mathit{100}}$

$$\begin{gathered} A_2=y\times F_2\times \frac{D_2}{100} \\ =y\times 100\times \frac{24}{100} \\ =₹24y \end{gathered}$$

Step 6: Calculate the difference in the annual incomes of Ram

As it is mentioned that there is a change of $₹1920$ in the annual income of Ram.

∴ $\mathit{D}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{a}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathit{i}\mathit{n}\mathit{c}\mathit{o}\mathit{m}\mathit{e}\mathit{s}={\mathit{A}}_{\mathbf{2}}\mathbf{-}\mathbf{}{\mathit{A}}_{\mathbf{1}}$

$$\begin{gathered} 1920=24y-8640 \\ 24y=1920+8640 \\ 24y=10560 \\ y=\frac{10560}{24} \\ y=440\mathrm{shares} \end{gathered}$$

Step 7: Calculate the market value of Golmal Entertainment's shares of Ram

$\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{=}\mathit{}\frac{\mathit{I}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}{\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}}$

$$\begin{gathered} M_2=\frac{SaleProceedsofRam}{y} \\ {M}_2=\frac{66000}{440} \\ {M}_2=₹150 \end{gathered}$$

Hence, Option C is correct because Ram bought the Golmal Entertainment shares at $\mathbf{₹}\mathbf{150}$.