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?

Answer 1

Hint: First consider cost price % as 100% then find sale price %. Then as it is given, the sale price is ₹ 392, compare it to find cost price and hence find profit by subtracting cost price from sale price.

Complete step by step answer:
In this question we are informed that the shopkeeper expects a gain of 22.5% on his cost price. Now if the sale was of ₹ 392 in this week then we have to find his profit.
As we are given the value of sale so we can consider the sale value as selling price.
So the selling price is ₹ 392.
Now let’s consider the cost price as 100%. Now we will use the equation, Cost price in % terms = Profit in % terms is equal to selling price in % terms.
So the Cost price in % terms is 100%, profit in % terms is 22.5% so we can say the selling price in % is 122.5%.
Now if the original cost is considered as ‘x’, then the selling price in terms of ‘x’ will be considered as\[\dfrac{122.5}{100}x\] or \[\dfrac{1225}{1000}x\].
Now as we already know the selling price is ₹ 392. So we can write the equation as,
\[\begin{align}
  & \dfrac{1225}{1000}x=392 \\
 & \Rightarrow ~x=\text{ }392\times \dfrac{1000}{1225}~=\text{ }320 \\
\end{align}\]
So, the cost price was ₹ 320. Now as we know that the cost price which is ₹ 320 and the selling price which is ₹ 392, so we can find profit using formula,
Profit = Selling Price – Cost Price
Profit = ₹392 - ₹ 320
Profit =₹72.
So, the Profit is ₹72.

Note: Students should know how to compare and find sale percent using profit present and cost price percent. They should also know how to find profit if the sale price and cost price is given.