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A and B start a business with investments of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of a year, they earn a profit of Rs. 5080. Find the share of each member in the profit ?

A. A = Rs. 1400, B = Rs. 1900, C = Rs. 1780 B. A = Rs. 1600, B = Rs. 1800, C = Rs. 1680 C. A = Rs. 1800, B = Rs. 1500, C = Rs. 1780 D. A = Rs. 1680, B = Rs. 1600, C = Rs. 1800 Answer: Option B
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Solution(By Apex Team)

A : B : C (5000 × 4 + 2500 × 8) : (4500 × 6 + 3000 × 6) : (7000 × 6) = 40000 : 45000 : 42000 = 40 : 45 : 42 $\begin{aligned}&\therefore\text{ A’s share }\\ &=\text{ Rs. }\left(5080\times\frac{40}{127}\right)\\ &=\text{ Rs. }1600\\ &\therefore\text{ B’s share }\\ &=\text{ Rs. }\left(5080\times\frac{45}{127}\right)\\ &=\text{ Rs. }1800\\ &\therefore\text{ C’s share }\\ &=\text{ Rs. }\left(5080\times\frac{42}{127}\right)\\ &=\text{ Rs. }1680\end{aligned}$

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