A, B and C invested money in the ratio of 1/2:1/3:1/5 in a business. After 4 months A doubled his investment and after 6 months B halves his investment. If the total profit at the end of the year be Rs. 34650 then find the share of each in profit ?

Answer: Option C

Ratio of capital invested by
$$\text{A, B and C}=15:10:6$$
Total capital invested by A in 1 year
$$\begin{array}{rl}& =15x\times 4+30x\times 8\\ & =300x\end{array}$$
Total capital invested by B in 1 year
$$\begin{array}{rl}& =10x\times 6+5x\times 6\\ & =90x\end{array}$$
Total capital invested by C in 1 year
$$\begin{array}{rl}& =6x\times 12\\ & =72x\end{array}$$
Ratio of profits:

A	:	B	:	C
300x	:	90x	:	72x
50x	:	15x	:	12x

According to the question,
$$\iff \left(50x+15x+12x\right)$$     = $$\text{Rs}\text{. 34650}$$
$$\begin{array}{rl}& \iff 77x=\text{Rs}.34650\\ & \iff x=\text{Rs}\text{. }\frac{34650}{77}\\ & \iff x=\text{Rs}\text{. }450\\ & \text{Profit of A}=\text{Rs}\text{. }450\times 50\\ & =\text{Rs}\text{. 22500}\\ & \text{Profit of B}=\text{Rs}\text{. }450\times 15\\ & =\text{Rs}\text{. 6750}\\ & \text{Profit of C}=\text{Rs}\text{. }450\times 12\\ & =\text{Rs}\text{. 5400}\end{array}$$