Question

A man sold two shirts at Rs 800 each. On one shirt he gains 25% and at the other he loses 20%. How much does he gain or lose in the whole transaction?

Answer 1

Hint:
Cost Price (C.P.): Price at which an article is purchased.
Selling Price (S.P.): Price at which an article is sold by a shopkeeper.
If the selling price is more than the cost price then it is known as profit.
$Profit = S.P.({\text{Selling price}}) - C.P.({\text{Cost price}})$
If the selling price is less than the cost price then it is known as loss.
$Loss = C.P.({\text{ Cost price}}) - S.P.({\text{Selling price}})$
Profit percentage is calculated on cost price.
$Profit\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
Loss percentage is calculated on cost price.
$Loss\% = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100$
This question is based on the definition of cost price and selling price. The formula used are
$
  Selling{\text{ }}price = C.P.\left( {\dfrac{{100 + \% Gain}}{{100}}} \right) \\
  Selling{\text{ }}price = C.P.\left( {\dfrac{{100 - \% Loss}}{{100}}} \right) \\
$

Complete step by step solution:
 This type of question is solved by using formula.
The cost price of two shirts = $2 \times Rs.800$
$ = Rs.1600$
The selling price of first shirt =$C.P.\left( {\dfrac{{100 + \% gain}}{{100}}} \right)$
\[
= 800 \times \left( {\dfrac{{100 + 25}}{{100}}} \right) \\
= 8 \times 125 \\
= Rs.1000 \\
\]
The selling price of second shirt = $C.P.\left( {\dfrac{{100 - \% loss}}{{100}}} \right)$
$
= 800 \times \left( {\dfrac{{100 - 20}}{{100}}} \right) \\
= 8 \times 80 \\
= Rs{\text{ }}640 \\
$
The total selling price of two shirts = S.P. of 1st shirt + S.P. of 2nd shirt
$
= Rs.1000 + Rs.640 \\
= Rs.1640 \\
$
Here, S.P.>C.P.
So, case of profit
Hence Gain$ = S.P. - C.P.$
$
= Rs.1640 - Rs.1600 \\
= Rs.40 \\
$
Hence, in the whole transaction there is a gain of Rs 40.

Note:
This question is a formula based question. The main step of this question is to calculate the selling price separately and finally add them. In this way we can calculate gain or loss in the whole transaction.
For profit, the selling price should be more than the cost price while for loss, cost price should be more than the selling price.