Question

In a certain store, the profit is \[{\text{32}}0\% \] of the cost. If the cost increases by \[{\text{2}}5\% \] but the selling price remains constant approximately. What percentage of the selling price is the profit? 

A. 30%

B. 100%
C. 70%
D. 250%

Answer 1

Hint: In the question, it is given that the profit is $320\%$. We will get profit only when Selling price is more than Cost price.

From the given data, we have to find a numeric relation between selling price and profit.  We use basic concepts in percentages along with the below formula and find the required answer.

Formula used:

1. Profit $=$ Selling Price $-$ Cost Price; which means Selling price = Cost Price + Profit.

2. Percentage of profit in selling price = \[\dfrac{{\text{Profit}}}{{\text{Selling Price}}} \times 100\].

Complete step-by-step answer:
Given in the question:
Profit this store is earning from the sale of one product = 320% of the product cost.
Cost of the product has increased by 25%.
Selling price remains the constant.
 Let us assume C.P be the cost price of the product which is C.P=100Rs.
Also it is given that, Profit comes out to be 320% of the product cost which is Profit = 320Rs.
Here, S.P be selling price of the product which is calculate using the formula selling price = Cost Price + Profit
So, S.P = \[100 + 320\]
By simplifying we get, S.P = 420Rs.
As, we know cost price increases by 25%
Therefore, C.P = 125% of original cost of the product
Hence, C.P = \[\dfrac{{125}}{{100}} \times 100\]
By cancelling 100 from both numerator and denominator we get,
C.P = \[125\]Rs.
As, it is given that after increasing the cost, the selling price remains constant.
So, S.P = 420Rs.
Therefore, new profit after increasing the cost will be calculated by the formula Profit = Selling Price - Cost Price.
Hence, profit = 420 – 125
By simplifying we get,
Profit = 295Rs.
Percentage of the selling price is the profit = \[\dfrac{{Profit}}{{Selling\,{\rm{ }}Price}} \times 100\] .
So, required percentage = \[\dfrac{{295}}{{420}} \times 100\]
On simplifying we get, Required % = 70% (approximately)
So, option (C) is correct.

Note: To solve these types of questions you can use the basic formulas of profit, selling price, cost price, and profit percentage. Similarly, questions can be come to calculate loss and loss percentage. With the help of this method you can easily solve it.