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 ?

Answer: Option C

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
$$\begin{array}{rl}& =2x\times 12:x\times 8:2x\times 6\\ & =6:2:3\end{array}$$
Sum of the terms of ratio
$$6+2+3=11$$
If the total profit at the end of the year be Rs. a
Then share of C
$$\begin{array}{rl}& \Rightarrow \frac{3a}{11}=2460\\ & \Rightarrow 3a=2460\times 11\\ & \Rightarrow a=\frac{2460\times 11}{3}\\ & \Rightarrow a=\text{Rs}\text{.}9020\end{array}$$