Question

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?

• A. Rs. 102,500
• B. Rs. 93,750
• C. Rs. 74,250
• D. Rs. 75,000
• E. Rs. 80,200

Answer 1

The Correct Option is D

To solve this problem, let's break it into steps:

1. Total profit = Rs. 2 lakhs.
2. Let the part of the profit shared between Y and Z (in the ratio of 2:3) be Rs. P.
3. Then, part of the profit distributed among X, Y, Z = Rs. (2,00,000 - P).
4. Share of Y and Z in Rs. P:
   Y's share = \( \frac{2}{5} \times P \)
   Z's share = \( \frac{3}{5} \times P \).
5. Share of X, Y, Z in remaining profit (2,00,000 - P) is divided by initial investments ratio.
6. Initial investment ratio, X:Y:Z = 2.5:3.5:4 = 5:7:8.
7. Hence, X's share = \( \frac{5}{20} \times (2,00,000 - P) \),
   Y's share = \( \frac{7}{20} \times (2,00,000 - P) \),
   Z's share = \( \frac{8}{20} \times (2,00,000 - P) \).
8. Z's total share = \( \frac{3}{5} \times P + \frac{8}{20} \times (2,00,000 - P) \).
9. X's total share = \( \frac{5}{20} \times (2,00,000 - P) \).
10. According to the problem, Z's amount is 4 times X's amount:
    \[ \frac{3}{5} \times P + \frac{8}{20} \times (2,00,000 - P) = 4 \times \left(\frac{5}{20} \times (2,00,000 - P)\right) \]
11. Simplifying, \( Z = \frac{3}{5} \times P + \frac{8}{20} \times (2,00,000 - P) = \frac{2(2,00,000 - P)}{5} \).
12. Solving: \( \frac{3}{5}P + \frac{8}{20}(2,00,000 - P) = \frac{8}{5}(2,00,000 - P) \).
13. \(- \frac{3P}{5} = -\frac{8}{5}P\), simplifying gives \( P = 1,00,000 \).
14. Total shared profit = Rs. 1,00,000 in ratio 2:3.
15. Y receives: \( \frac{2}{5} \times 1,00,000 = Rs. 40,000 \).
16. Remaining profit shared in original investment ratio:
17. Remaining profit = 2,00,000 - 1,00,000 = 1,00,000.
18. Y's share from remaining profit = \( \frac{7}{20} \times 1,00,000 = 35,000 \).
19. Total amount Y receives = 40,000 + 35,000 = Rs. 75,000.

Thus, the amount Y receives is Rs. 75,000.