Ramesh had $₹ 100$ shares of 'Bihar Steel' paying $8 %$ dividend. He sold them at a market price of $₹ 130$ and invested the proceeds in buying $₹ 50$ shares of 'Jindal Steel' available at $₹ 75$ and paying $12 %$ dividend. He thus increased his annual income by $₹ 360$ . How many shares did Ramesh sell?

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Solution

Step 1: Given Data:
Nominal value of Bihar Steel's shares, $N_{1} = ₹ 100$
Dividend of Bihar Steel's shares, $D_{1} = 8 %$
Market value of Bihar Steel's shares, $M_{1} = ₹ 130$
Nominal value of Jindal Steel's shares, $N_{2} = ₹ 50$
Dividend of Jindal Steel's shares, $D_{2} = 12 %$
Market value of Jindal Steel's shares, $M_{2} = ₹ 75$
Increase in Ramesh's annual income $= ₹ 360$
Step 2: Calculate the sale proceeds of Ramesh:
Let us assume that the number of shares sold was $n_{1}$ .
$S a l e p r o c e e d s = N u m b e r o f s h a r e s \times M a r k e t v a l u e$
$= n_{1} \times M_{1} = n_{1} \times 130 = ₹ 130 n_{1}$
Step 3: Calculate the number of Jindal Steel's shares bought:
Let us assume that the number of shares bought was $n_{2}$ .
$N u m b e r o f s h a r e s = \frac{I n v e s t m e n t}{M a r k e t v a l u e}$
$n_{2} = \frac{S a l e p r o c e e d s}{M_{2}} = \frac{130 n_{1}}{75} = \frac{26 n_{1}}{15} shares$
Step 4: Calculate the annual income from Bihar Steel's shares sold:
$A n n u a l i n c o m e = N u m b e r o f s h a r e s \times N o m i n a l v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{1} = n_{1} \times N_{1} \times \frac{D_{1}}{100} = n_{1} \times 100 \times \frac{8}{100} = ₹ 8 n_{1}$
Step 5: Calculate the annual income from Jindal Steel's shares bought:
$A n n u a l i n c o m e = N u m b e r o f s h a r e s \times N o m i n a l v a l u e \times \frac{R a t e o f d i v i d e n d}{100}$
$A_{2} = n_{2} \times N_{2} \times \frac{D_{2}}{100} = \frac{26 n_{1}}{15} \times 50 \times \frac{12}{100} = ₹ \frac{104 n_{1}}{10}$
Step 6: Calculate the difference in the annual incomes of Ramesh:
As it is mentioned that there is an increase in the annual income therefore annual income from Jindal Steel's shares bought is greater than the Bihar Steel's shares sold.
∴ $D i f f e r e n c e i n a n n u a l i n c o m e s = A_{2} - A_{1}$
$= \frac{104 n_{1}}{10} - 8 n_{1} = \frac{104 n_{1} - 8 n_{1} \times 10}{10} = \frac{104 n_{1} - 80 n_{1}}{10} = ₹ \frac{24 n_{1}}{10}$
According to the question, the increase in Ramesh's income is $₹ 360$
$\Rightarrow 360 = \frac{24 n_{1}}{10}$
$\Rightarrow n_{1} = \frac{360 \times 10}{24} \Rightarrow n_{1} = 150 shares$
Final Answer: The number of shares sold by Ramesh is $150$ shares.

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Ramesh had ₹100 shares of 'Bihar Steel' paying 8% dividend. He sold them at a market price of ₹130 and invested the proceeds in buying ₹50 shares of 'Jindal Steel' available at ₹75 and paying 12% dividend. He thus increased his annual income by ₹360. How many shares did Ramesh sell?