Question

Arjun invested for Rs. 60,000 in \[12\%\], Rs. 100 in shares quoted at RS.125. When the market value of these rose to Rs. 140 each, he sold enough shares to raise Rs. 11,200. Calculate
I.The number of shares he still holds.
II.The annual income on these shares.

Answer 1

Hint: Here we will proceed by firstly finding the market value of one share using the concept that the market value of 1 share is Rs 100 which is quoted as Rs 125. Then we have to calculate the number of shares he still holds which also helps to find the annual income per share.

Complete step by step solution:
(i) Given investment by the man \[=\,\text{Rs}.\,60,000\]
Market value of 1 share \[=\,\text{Rs}.\,125\]
Therefore, number of shares purchased \[=\dfrac{60000}{125}=480\] shares
So, for the First part of the question we have to find the nominal values
If Nominal values of 1 share \[=\,\text{Rs}.\,100\]
Then, Nominal Values of 360 shares \[=\,\text{Rs}.\,100\times 360=\text{Rs}.\,36,000\]
Now, we have to find the number of shares sold for which we need to assign a variable to it.
Consider the number of shares sold \[=n\]
sale price of 1 share \[=\,\text{Rs}.\,140\]
He sold enough shares to raise Rs. 11,200. That means,
Total sale price of n shares \[=\,\text{Rs}.\,11,200\].
We can also write in the form of expression that is \[140n=11,200\]
Then \[n=\dfrac{11,200}{140}=80\] shares
The number of shares he still holds \[=480-80=400\].

(ii) Now, we need to find the second part of the question, which is annual income per share.
For that we need to know about Face value of 1 share
That is Face value of 1 share is Rs. 100. And also Dividend is given in the question that is \[12\%\]
And the number of shares we calculated in the first part is 400 shares.
By using the Formula of Annual income \[\text{Annual}\,\text{income}\,\text{per}\,\text{share}=\left( \text{number of shares} \right)\,\times \left( \text{rate of dividend} \right)\times \left( \text{Nominal or Face value of 1 share} \right)\]
Therefore, by substituting all the values in the above formula.
 \[\text{Annual}\,\text{income}\,\text{per}\,\text{share}=400\times \left( \dfrac{12}{100} \right)\times 100\]
By simplifying Further, we get:
\[\text{Annual}\,\text{income}\,\text{per}\,\text{share}=400\times 15=\text{Rs}\text{.}\,4,800\].

Note: The face value of rupees hundred in this dilemma signifies that the face value of one share is equal to Rs 100. If the question is to discover the dividend % per share for any company, the answer is to divide the yearly dividend or the dividend at the end of the year by the total number of shares held by the man.