Question

A man invested \[Rs.35,000\] in \[10\% \] \[Rs.200\] shares quoted at \[Rs.120\] . When the market value of these shares rose to \[Rs.150\], he sold some shares, just enough to raise \[Rs.12000\] . Calculate the number of shares he still holds.
A. \[211.66\]
B. \[209.66\]
C. \[209.66\]
D. \[80\]

Answer 1

Hint: In order to find the answer to the question, we have to first calculate the number of shares that the man purchased. After which we have to find the number of shares that the man sold. In the last step, we have to simply subtract the number of shares sold from the number of shares purchased.

Formula used:
The formulas that will be used to solve the above questions are
\[{\text{Number of shares purchased = }}\dfrac{{{\text{money invested}}}}{{{\text{market value of each share}}}}\] .
\[{\text{Number of shares sold = }}\dfrac{{{\text{amount received}}}}{{{\text{market value of each share}}}}\] .
\[{\text{Number of shares held by the man = Number of shares purchased - Number of shares sold}}\] .

Complete step by step solution:
First, we will find the total amount of shares bought by the man. For this we will use the first formula.
\[{\text{Number of shares purchased = }}\dfrac{{{\text{money invested}}}}{{{\text{market value of each share}}}}\]
We are given,
The man invested \[Rs.35,000\] .
The market value of each share was: \[Rs.120\] .
So, \[{\text{Number of shares purchased = }}\dfrac{{35000}}{{120}}\]
\[ = 291.66\] .
Now, let the number of shares sold by the man be \[x\] .
To calculate the total number of shares sold by him, we will use the second formula
\[{\text{Number of shares sold = }}\dfrac{{{\text{amount received}}}}{{{\text{market value of each share}}}}\]
So, \[{\text{Number of shares sold = }}\dfrac{{12000}}{{150}}\]
\[ = 80\] .
Hence, the number of shares the man still holds are:
\[{\text{Number of shares held by the man = Number of shares purchased - Number of shares sold}}\]
 \[
  {\text{ = 291}}{\text{.66 - 80}} \\
   = 211.66 \\
 \]
Therefore, the number of shares which the man still holds are \[211.66\] .
So, the correct answer is Option A.

Note: To solve the questions involving shares, we must always remember the formulas. In the absence of these formulas we cannot derive the correct answers. These formulas help in calculating the answer within a very short amount of time and with high levels of accuracy. In this solution, we have used three such formulas to get the answer.