GMAT Quant Questions | Ratio Proportion Q2

GMAT Sample Questions | Ratio Proportion | Word Problem

The given question is a GMAT 600 - 650 arithmetic question from the topic Ratio & Proportions. This GMAT sample question tests the concept of division on profits based on proportion of investment made. A partnership question.

Question 2: Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?

  1. $2000
  2. $6000
  3. $4000
  4. $1333
  5. $3000

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Explanatory Answer | GMAT Partnership Question 2

Step 1 of solving this GMAT Ratio Question: Deduce profit for Effort and Investments

Total profit earned will be divided into two parts: \\frac{1}{3}) will be for efforts and \\frac{2}{3}) for investments made.
Mary and Mike get equal share for their efforts.
If x is the share that each of Mike and Mary get for efforts, 2x is the share of profit for total efforts.
\\frac{1}{3}) of total profit goes toward effort.
Hence, the total profit earned will be 6x.

profit tree diagram

Step 2 of solving this GMAT Ratio Question: Share of profit for investments made

4x is the profit to be distributed for investments made.
4x will be divided in the ratio of amount invested by Mary and Mike.
As Mary and Mike invested $700 and $300 respectively, share of profit on investments will be divided in the ratio 7 : 3
Hence, if Mary receives 7y, Mike will receive 3y.
Total profit on investments is 10y which is equal to 4x
10y = 4x ... (1)

Step 3 of solving this GMAT Ratio Question: Compute total profit earned

Difference between amount shared between Mike and Mary is $800.
7y − 3y = 800
y = $200
Total profits on investment 10y = 2000
From equation 1, 10y = 4x
So, x = \\frac{2000}{4}) = $500
Total profit earned 6x = $3000

Choice E is the correct answer.

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