Discussion
A, B and C enter into partnership by investing ₹ 1,500, ₹ 2,500, ₹ 3,000, respectively. A as a Manager gets one-tenth of the total profit and the remaining profit is divided among the three in the ratio of their investments. If share of A is ₹ 369, find the shares of B and C?
Answer: A
B and C receive ₹ 405 and ₹ 486.
Let the total profit be \(P\). A gets \(P/10\) as manager, and the remaining \(0.9P\) is shared 1500 : 2500 : 3000 = 3 : 5 : 6:
\[ \begin{aligned} 0.1P + 0.9P \times \tfrac{3}{14} &= 369 \\ P\left(\tfrac{14 + 27}{140}\right) &= 369 \Rightarrow P = 1260 \end{aligned} \]
The shared part is 1,134. B gets \(1134 \times 5/14 = 405\) and C gets \(1134 \times 6/14 = 486\). Option C lists the same amounts the other way round, giving C the smaller share though C invested more.
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