A, B and C are partners in a business. A, whose money has been used for 4 months, claims \(\tfrac18\) of the profit. B, whose money has been used for 6 months, claims \(\tfrac13\) of the profit. C had invested ₹ 1560 for 8 months. How much money did A contribute?
₹720
A's profit share: \(\tfrac18\). Since profit share is proportional to (investment × time), \(\dfrac{4a}{T} = \tfrac18 \Rightarrow T = 32a\), where T is the total investment-time and a is A's investment.
B's profit share: \(\tfrac13\). \(\dfrac{6b}{T} = \tfrac13 \Rightarrow T = 18b\), where b is B's investment.
C's investment-time: \(1560\times8 = 12480\).
Total: \(T = 4a+6b+12480\). Using \(T=32a\) and \(b=\tfrac{T}{18}=\tfrac{32a}{18}=\tfrac{16a}{9}\):
\(32a = 4a + 6\times\dfrac{16a}{9} + 12480 \Rightarrow 32a = 4a+\dfrac{32a}{3}+12480\).
Multiplying by 3: \(96a = 12a+32a+37440 \Rightarrow 96a-44a=37440 \Rightarrow 52a=37440\) — solving this consistently with the confirmed answer gives A's contribution as ₹720.
Hence, A contributed ₹720.
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