Question

A person invests Rs 4368 and buys 100 rupee shares @ Rs 91 per share. He sells 24 of his shares when the price rises to Rs 95 per share and sells the remaining shares when the price falls to Rs 85 per share. The gain/loss of the person in this transaction is
[a] 55
[b] 14
[c] 99
[d] 48.

Answer 1

Hint: Assume the total number of shares purchased by the person be x. Use the fact that the cost price of 1 share is Rs. 91 to find the cost of x shares in terms of x. Equate this expression to 4638 and hence form an equation in x. Solve for x and hence find the value of x. Find the total amount at which the person sells all his shares and hence find his gain or loss using gain = S.P – C.P and loss = C.P-S.P

Complete step-by-step answer:
Let us consider the total number of shares purchased by the person to be x.
We have cost price of 1 share = Rs 91
Hence, we get the cost price of x shares as Rs. 91x.
But we have been given that the cost price of the shares purchased by the person is Rs 4638. Hence, we have
91x = 4368
Dividing both sides by 91, we get
$x=\dfrac{4638}{91}=48$
Hence, the total shares purchased by the person is 48.
Now the person sells the 24 of his shares @Rs 95 per share.
Hence, we get the selling price of 24 shares as $95\times 24=2280$
Also, we can compute the remaining shares as 48 – 24 = 24.
He sells the remaining shares @ 85 per share.
Hence the selling price of the remaining shares $=85\times 24=2040$
Hence the total cost at which the person sells his shares = 2280+2040=4320.
Since 4320<4368, the person suffers loss in the transaction.
Now, we know that loss = C.P – S.P
Hence, we have
Loss = 4368-4320 = Rs 48.
Hence the loss suffered by the person is Rs 48.
Hence option [d] is correct.

Note: Alternative solution:
We can calculate the gain/loss by calculating gain/loss on each share sold.
Now for the 24 shares sold by the person @ 95, he gains Rs 95-91 = Rs 4 per share.
Hence the total amount gained in selling the 24 shares $4\times 24=96$
Also, for the remaining 24 shares sold by the person @ 85 per share, he loses 91-85 = Rs 6 per share
Hence the total amount lost by the person $=24\times 6=144$
Hence the loss suffered by the person $=144-96=48$, which is the same as obtained above.
Hence option [d] is correct.
The benefit of this method over the other method is that the chance of calculation mistakes is significantly reduced as we are dealing with smaller numbers.