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?

Accepted Answer

D. 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 $5k$. Y gets $2k$, Z gets $3k$. Remaining profit = $200000 - 5k$. X receives: $\frac{5}{20}(200000 - 5k) = \frac{1}{4}(200000 - 5k)$. Z receives: $3k + \frac{8}{20}(200000 - 5k) = 3k + \frac{2}{5}(200000 - 5k)$. Given $Z = 4X$: $3k + \frac{2}{5}(200000 - 5k) = 4 	imes \frac{1}{4}(200000 - 5k) = 200000 - 5k$. $3k + 80000 - 2k = 200000 - 5k \implies k + 80000 = 200000 - 5k \implies 6k = 120000 \implies k = 20000$. Y receives = $2k + \frac{7}{20}(200000 - 5k) = 40000 + \frac{7}{20}(100000) = 40000 + 35000 = 	ext{Rs. } 75,000$.

Profit Sharing Ratio

Explanation

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