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

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