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A started a business with the capital of Rs. 500. After 2 months B joined A with Rs. 400. 6 months after the business started C joined with Rs. 800. If the total profit earned at the end of the year is Rs. 444 find the share of their profit ?

a) Rs. 180, Rs. 120, Rs. 144
b) Rs. 150, Rs. 130, Rs. 123
c) Rs. 160, Rs. 141, Rs. 125
d) Rs. 141, Rs. 110, Rs. 140

Answer: a
Explanation:
    A     :     B     :     C  
Capital   500 : 400 : 800
  × : × : ×
Time 12 : 10 : 6
Profit   6000 : 4000   4800
  15 : 10 : 12

$$\eqalign{ & \left( {15 + 10 + 12} \right){\text{units}} = {\text{Rs}}{\text{.}}\,{\text{444}} \cr & {\text{37 units}} = {\text{Rs}}{\text{. 444}} \cr & 1{\text{ unit}} = \frac{{444}}{{37}}{\text{ = Rs}}{\text{. 12}} \cr & {\text{Profit of A}} = 12 \times 15 = {\text{Rs}}{\text{.}}\,{\text{180}} \cr & {\text{Profit of B}} = 12 \times 10 = {\text{Rs}}{\text{.}}\,{\text{120}} \cr & {\text{Profit of C}} = 12 \times 12 = {\text{Rs}}{\text{.}}\,{\text{144}} \cr} $$

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