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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 Rajeev
B. What is his yearly income?
C. If he sells \[60%\] of his shares when price rises to Rs.\[90\], calculate his gain in transaction.

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Last updated date: 13th Jun 2024
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Answer
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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.