In a business, B invests half the amount invested by A. After 6 months from the start of the business, C joins the business with an amount equal to twice of B’s investment. After 8 months from the start of the business B withdraws completely from the business. If at the end of the year, C’s share in the profit was Rs. 2460, what was the total profit received that year ?

A. Rs. 11200 B. Rs. 9600 C. Rs. 9020 D. Rs. 12000 Answer: Option C
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Solution(By Apex Team)

Let B’s investment be Rs. x ∴ A’s investment be Rs.2x ∴ C’s investment be Rs.2x A invests money for 12 months B invests money for 8 months C invests money for 6 months Ratio of the equivalent capitals of A, B and C for 1 month $\begin{array}{l} =2 x \times 12: x \times 8: 2 x \times 6\\ =6: 2: 3\\ \text { Sum of the terms of ratio }\\ 6+2+3=11 \end{array}$ If the total profit at the end of the year be Rs. a Then share of C $\begin{aligned}&\Rightarrow\frac{3a}{11}=2460\\ &\Rightarrow3a=2460\times11\\ &\Rightarrow a=\frac{2460\times11}{3}\\ &\Rightarrow a=\text{ Rs. }9020\end{aligned}$

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