In a Certain Store, the Profit is 320% of the Cost GMAT Problem Solving

Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

1. 30
2. 70
3. 100
4. 150
5. 250

“In a certain store, the profit is 320% of the cost.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

This problem can be solved using the basic concept of profit and loss along with percentage. In the given question, it is stated that the store earned profit from the sale of 1 product = 320% of the cost product(CP). CP increased by 25%, whereas the Selling price(SP) remained unchanged.
Let us consider those C.P=100 rupees.
The question also states that the profit comes out to be 320% of the CP.
So, Profit = 320 rupees.
Here, S.P = Cost Price + Profit
So, S.P = 100+320
Simplifying both sides we get,
S.P = 420 rupees.
As, the question states that the cost price increases by 25%
Therefore, C.P = 125% of the original cost of the product

Hence, C.P = \(\frac{125}{100}*100\)

Equating both sides we get,
C.P = 125 rupees.
As the question states that after increasing the cost, the selling price remains constant.
So, S.P = 420 rupees.
So, the net profit becomes
Profit = SP - CP
Which implies 420-125 = 295 rupees.

Therefore, the percentage of the SP is the profit =\( \frac{Profit}{SP}×100\)

So the required percentage is \(\frac{295}{420}×100\) = 70%

Thus the percentage of the selling price is the profit is 70%. 

Correct Answer: B

Approach Solution 2:

Let the CP= 100 rupees
Then the required profit = 320 rupees.
SP = 420 rupees.
New CP = 125% of 100 rupees = 125 rupees.
Therefore new SP = 420 rupees
Hence, profit = (420-125) rupees = 295 rupees

So the required percentage is \(\frac{295}{420}×100\) = 70%

Thus the percentage of the selling price is the profit is 70%. 

Correct Answer: B

Approach Solution 3:

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 = 125/100×100

By cancelling 100 from both numerator and denominator we get,
C.P = 125125 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 = Profit/SellingPrice×100

So, required percentage = 295/420×100

On simplifying we get, Required % = 70% (approximately)

Correct Answer: B

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