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# Rajeev invests Rs. $9750$ in shares of a company paying $15\dfrac{1}{2}%$ dividend per annum when the market value of each share of Rs.$50$ is Rs.$65$.A. Find the shares purchased by RajeevB. What is his yearly income?C. If he sells $60%$ of his shares when price rises to Rs.$90$, calculate his gain in transaction.

Last updated date: 21st Jul 2024
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Hint:To find the number of shares purchased by Rajeev we use the formula:
Number of share bought $=\dfrac{\text{Investment}}{\text{Market Value}}$
And to find the yearly income, we get the formula as:
The yearly income generated as $=\text{Number of Share}\times \text{Rate of Dividend}\times \text{Nominal Value}$
And to find the final part of the gain when $60%$ of the share is:
$\left( \text{Number of Share}\times \text{Market Value}{{\text{e}}_{90}} \right)-\left( \text{Number of Share}\times \text{Market Value}{{\text{e}}_{65}} \right)$

Complete step by step solution:
According to the question given, the investment given by Rajeev is Rs.$9750$. The dividend paid by the investment is given as $15.5%$.
Now to find the number of shares by Rajeev, we use the formula where we divide the sum invested by the market value of a single share:
Number of share bought $=\dfrac{\text{Investment}}{\text{Market Value}}$
Number of share bought $=\dfrac{Rs.9750}{Rs.65}$
Number of share bought $=150$
Placing the values, we get the total number of shares as $150$.
The total yearly income of the sum invested by Rajeev is found by the product of total number of shares, rate of dividend and nominal value of one share as:
The yearly income generated as $=\text{Number of Share}\times \text{Rate of Dividend}\times\text{Nominal Value}$
Placing the values in the above formula we get the yearly income as:
The yearly income generated as $=\text{150 }\!\!\times\!\!\text{ }\dfrac{15.5}{100}\text{ }\!\!\times\!\!\text{ 50}$
$\Rightarrow \text{150 }\!\!\times\!\!\text{ }\dfrac{15.5}{100}\text{ }\!\!\times\!\!\text{ 50}$
$\Rightarrow$ Rs.$1162.50$
Now as we have got the income and the number of shares, we now find the gain on his $60%$ of his shares when price rises to Rs.$90$ is:
Now the total number of shares from his $60%$ share is:
$\Rightarrow \dfrac{60}{100}\times 150$
$\Rightarrow \dfrac{60}{100}\times 150=90$ shares
Therefore, the total price gain is $=\left( \text{Number of Share}\times \text{Market Value}{{\text{e}}_{90}} \right)-\left( \text{Number of Share}\times \text{Market Value}{{\text{e}}_{65}} \right)$.
$\Rightarrow 90\times 90-90\times 65$
$\Rightarrow 2250$ Rupees
Therefore, the profit gained when Rajeev sold $60%$ of his share is Rs. $2250$.

Note: Dividend is the annual profit of a company, shareholders when shares are bought at a certain market value. The market value of a share depends upon the company’s performance.