### 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 ?

A. Rs. 7200 B. Rs. 5800 C. Rs. 4000 D. Rs. 4800 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 $\begin{array}{l} \Rightarrow \text { Profit of } \mathrm{A} \text { : Profit of } \mathrm{B}: \text { Profit of } \mathrm{C}\\ \Rightarrow 2400 \times 12:(3600 \times 8)+(3000 \times 4): \mathrm{X} \times 8\\ \Rightarrow 28800: 40800: 8 \mathrm{X}\\ \Rightarrow 3600: 5100: \mathrm{X} \end{array}$ Given profit of C = Rs. 8000 And total profit of A, B and C = Rs. 22500 \begin{aligned}&\therefore\frac{\mathrm{X}\times22500}{3600+5100+\mathrm{X}}=8000\\ &\Rightarrow\frac{\mathrm{X}\times22500}{8700+\mathrm{X}}=8000\\ &\Rightarrow22500\mathrm{X}=69600000+8000\mathrm{X}\\ &\Rightarrow14500\mathrm{X}=69600000\\ &\Rightarrow\mathrm{X}=\mathrm{Rs}.4800\end{aligned}