A and B started a business by investing Rs. 2400 and Rs. 3600 respectively. At the end 4th months from the stat of the business, C joined with Rs. X. After 8 months from the start of the business, B withdrew Rs. 600. If C's share is Rs. 8000 in the annual profit of Rs. 22500, what was the amount C invested in the business ?

Answer: Option D

A invests Rs. 2400 for 12 months
B invests Rs. 3600 for 8 months
And Rs. 3000 for 4 months
C invests Rs. X for 8 months
Ratio of profit of A, B and C
$$\Rightarrow \text{Profit of A}$$   : $$\text{Profit of B}$$   : $$\text{Profit of C}$$
$$\Rightarrow \text{2400}\times \text{12}$$   : $$\left(3600\times 8\right)$$   + $$\left(3000\times 4\right)$$   : $$\text{X}\times 8$$
$$\begin{array}{rl}& \Rightarrow 28800:40800:8\text{X}\\ & \Rightarrow 3600:5100:\text{X}\end{array}$$
Given profit of C = Rs. 8000
And total profit of A, B and C = Rs. 22500
$$\begin{array}{rl}& \therefore \frac{\text{X}\times 22500}{3600+5100+\text{X}}=8000\\ & \Rightarrow \frac{\text{X}\times 22500}{8700+\text{X}}=8000\end{array}$$
$$\Rightarrow 22500\text{X}$$   = $$69600000$$   + $$8000\text{X}$$
$$\begin{array}{rl}& \Rightarrow 14500\text{X}=69600000\\ & \Rightarrow \text{X}=\text{Rs}.4800\end{array}$$