Question

A shopkeeper expects a gain of 22.5 % on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
(a). Rs. 18.20
(b). Rs. 70
(c). Rs. 72
(d). Rs. 88.25

Answer 1

Hint: The formula to calculate the gain percentage of a sale is \[Gain\% = \dfrac{{SP - CP}}{{CP}} \times 100\% \]. Use this formula and substitute the given values to find the cost price of the sale. Then calculate the profit by finding the difference between the selling price and cost price.

Complete step by step answer:

In this problem, it is given that the shopkeeper expects a gain of 22.5 % on his cost price, and in a week, his sale was of Rs. 392.
Hence, the selling price is given as Rs. 392.
SP = Rs. 392
Let the cost price of the sale be CP.
We know that the formula to calculate gain percent is given as follows:
\[Gain\% = \dfrac{{SP - CP}}{{CP}} \times 100\% \]
The gain percent is given as 22.5 %, hence, we have:
\[22.5\% = \dfrac{{392 - CP}}{{CP}} \times 100\% \]
Simplifying the above equation, we have as follows:
\[\dfrac{{22.5}}{{100}}CP = 392 - CP\]
\[0.225CP = 392 - CP\]
Taking all terms containing CP to the left-hand side of the equation, we get:
\[0.225CP + CP = 392\]
Solving for CP, we have:
\[1.225CP = 392\]
\[CP = \dfrac{{392}}{{1.225}}\]
\[CP = Rs.320\]
The profit is the difference between the selling price and the cost price. Hence, we have:
Profit = SP – CP
Profit = 392 – 390
Profit = Rs. 72
Hence, the correct answer is option (c).

Note: You should not take the profit as the gain percentage of the selling price. The gain is the gain percentage of cost price and hence, first, you need to find the cost price.