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Profit Sharing Ratio

XAT 2020 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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X, Y and Z start a web-based venture together. X invests Rs. 2.5 lakhs, Y invests Rs. 3.5 lakhs, and Z invests Rs. 4 lakhs. In the first year, the venture makes a profit of Rs. 2 lakhs. A part of the profit is shared between Y and Z in the ratio of 2:3, and the remaining profit is divided among X, Y and Z in the ratio of their initial investments. The amount that Z receives is four times the amount that X receives. How much amount does Y receive?

  1. A.

    Rs. 102,500

  2. B.

    Rs. 93,750

  3. C.

    Rs. 74,250

  4. D.

    Rs. 75,000

  5. E.

    Rs. 80,200

Answer

D

Explanation

Initial investments: X:Y:Z = 2.5 : 3.5 : 4 = 5 : 7 : 8. Sum of ratio = 20. Total profit = Rs 2,00,000. Let the special profit shared between Y and Z be 5k5k. Y gets 2k2k, Z gets 3k3k. Remaining profit = 200000−5k200000 - 5k. X receives: 520(200000−5k)=14(200000−5k)\frac{5}{20}(200000 - 5k) = \frac{1}{4}(200000 - 5k). Z receives: 3k+820(200000−5k)=3k+25(200000−5k)3k + \frac{8}{20}(200000 - 5k) = 3k + \frac{2}{5}(200000 - 5k).

Given Z=4XZ = 4X: 3k+25(200000−5k)=4×14(200000−5k)=200000−5k3k + \frac{2}{5}(200000 - 5k) = 4 \times \frac{1}{4}(200000 - 5k) = 200000 - 5k. 3k+80000−2k=200000−5k  ⟹  k+80000=200000−5k  ⟹  6k=120000  ⟹  k=200003k + 80000 - 2k = 200000 - 5k \implies k + 80000 = 200000 - 5k \implies 6k = 120000 \implies k = 20000.

Y receives = 2k+720(200000−5k)=40000+720(100000)=40000+35000=Rs. 75,0002k + \frac{7}{20}(200000 - 5k) = 40000 + \frac{7}{20}(100000) = 40000 + 35000 = \text{Rs. } 75,000.

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