Question: When the selling price of an article is increased by 20% and the cost remains the same, the profit increases by 50%. Find the profit percentage at which the item was being sold originally.

(A) 25%
(B) 33.33%
(C) 40%
(D) 50%
(E) 66.66%

Correct Answer: E
Solution and Explanation:
Approach Solution 1:
Let the original cost price of the item be x.
Let the original Selling price of the item be 100.
After increasing the SP by 20%, SP becomes 120.
Now, we know the profit increases by 50% when the SP has been increased.
Hence => Original Profit + 50% x Original Profit = New Profit
=> 1.5xOriginal Profit = New Profit {Since 50% = 50/100 = .5}
=> 1.5 x (Original SP - CP) = (New SP - CP)
=> 1.5 x(100-x) = (120 - x)
=> 150 - 1.5x = 120 - x
=> 30 = .5x
=> x=300/5
=> x = 60 ie. Cost Price is 60.
We now need to calculate the original profit % which is given by
(SP-CP)/CP x 100
=(100-60)/60 x 100
= 66.67%

Approach Solution 2:
Let the original CP = x
Let original SP = y
Profit = y - x
New SP = 20 more than original SP = 1.2y
New CP = Old CP = x
New Profit = (1.2y - x)
Given that the new profit is 50% more than that old profit.
(y - x )* 1.5 = 1.2y - x
1.5y - 1.5x = 1.2y - x
0.3y = 0.5x
x = 0.6y
Profit%= (SP-CP)/CP*100
=(y−x)/x*100
= (y−0.6y)/0.6y*100
Profit % =0.4/0.6*100= 66.67%

Approach Solution 3:
Given:
When the selling price of an article is increased by 20% and the cost remains the same, the profit increases by 50%.
Asked:
Find the profit percentage at which the item was being sold originally.
Let the cost price be c and original profit percentage be p%
Original selling price = c(100% + p%)
Increased selling price = c(100% + p%)1.2 = c(100% + 1.5p%)
120% + 1.2p% = 100% = 1.5p%
.3p% = 20%
p = 20/.3= 200/3= 66.66%

“When the selling price of an article is increased by 20% and the cost”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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