Question: The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?

1. 40%
2. 8%
3. 25%
4. 16.66%
5. 9%

Answer:
Approach Solution (1):
Original cost before weight adjustment: x
Cost after 90% weight adjustment:\({9\over10}x\)
20% profit on\({{9\over10}x}:{({120\over100})}{({9\over10})}(x)or{({108\over100})}x\)
Markup on original cost of x:\({{({108\over100}x)}\over{x-1}}={8\over100}\)
Correct option: B

Approach Solution (2):
The most natural way to deal with ‘weights’ questions is by assuming values
Say the trader’s balance shows 100 grams. It is actually 90 grams because it weighs 10% less. Say, the cost price is $90 ($1/gm). Since he gets profit of 20%, the selling price must be
\(90+{({120\over100})}*90=$108\)
Since the cost price is actually supposed to be $100 (for 100 grams) and the selling price is $108, the mark up is simply 8%
Correct option: B

Approach Solution (3):
Given: The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%
Asked: What is the mark up on the cost price?
Let the mark up on the cost price be x
\({{1\over0.9}}*(1+x)=1.2\)
\((1+x)=1.2*0.9=1.08\)
\(x =8\%\)
Correct option: B

“The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 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.

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