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 ?

Solution(By Examveda 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
$$\eqalign{ & = 2x \times 12:x \times 8:2x \times 6 \cr & = 6:2:3 \cr} $$
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
$$\eqalign{ & \Rightarrow \frac{{3a}}{{11}} = 2460 \cr & \Rightarrow 3a = 2460 \times 11 \cr & \Rightarrow a = \frac{{2460 \times 11}}{3} \cr & \Rightarrow a = {\text{Rs}}{\text{.}}\,9020 \cr} $$