Question: X & Y entered into partnership with $700 and $600 respectively. After 3 months, X withdrew 2/7 of his stock but after 3 months, he puts back 3/5 of what he had withdrawn. The profit at the end of the year is $726. If the profit was shared according to time weighted investment, then what was the difference between the profits of those two friends?
- $360
- $183
- $36
- $6
- $4
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
There is only one solution to this problem.
The problem statement informs that:
Given:
- X entered into partnership with $700.
- Y entered into partnership with $600.
- After 3 months, X withdrew 2/7 of his stock.
- After 3 months, he puts back 3/5 of what he had withdrawn.
- The profit at the end of the year is $726.
Condition:
- profit was shared according to time weighted investment.
Find Out:
- the difference between the profits of those two friends.
Since the funds change after 3 months in the initial 6 months, let’s inspect the quarterly investments.
First quarter: X=700, Y=600
X withdraws 2/7th after 3 months. Hence, he withdraws $200
Hence, in the Second quarter, the amounts are: X=700-200=500, Y=600
After 3 months, X puts back 3/5 of what he had withdrawn
Hence, Third and fourth quarters: X=500+120=620, Y=600
Investments:
X= 700 + 500 + 2*620 = 2440 and Y= 4*600= 2400
Therefore the ratio of X:Y = 2440:2400=61:60
This difference is 1 when the amount is 61+60=121. But the profit is 726.
Therefore, the difference is 726/121=6
So the difference between profits is $6.
“X & Y entered into partnership with $700 and $600 respectively”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This GMAT Quantitative reasoning section tests the numerical and analytical skills of the candidates. GMAT Problem Solving questions enable the candidates to evaluate facts and solve numerical problems. The GMAT Quant practice papers help the candidates to analyse different types of questions that will improve their mathematical understanding.
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