A, B and C started a business by investing Rs. 24000, Rs. 32000 and Rs. 18000 respectively. A and B are active partners and get 15% and 12% of total profit and remaining profit is to be distributed among them in the ratio of their investment. If C got total Rs. 65700 as a profit, what was the total amount of profit ?

A. Rs. 470000 B. Rs. 370000 C. Rs. 345000 D. Rs. 157000 Answer: Option B
\begin{aligned}\mathrm{A}&:&\mathrm{B}&\quad:&\mathrm{C}\\ \text{ Capital }\rightarrow24000&:&32000&:&18000\\ 24&:&32&:&18&\\ 12&:&16&:&9\end{aligned} \begin{aligned}&\text{Let the total profit}=100x\\ &\text{ Extra share of }\mathrm{A}\\ &=100x\times\frac{15}{100}\\ &=15x\\ &\text{Extra share of B}\\ &=100x\times\frac{12}{100}\\ &=12x\\ &\text{Remaining profit}\\ &=\left[100x-\left(15x+12x\right)\right]\\ &=73x\end{aligned} According to the question, Note: Remaining profit will be distributed in the ratio of their capitals. ∴ Share of C \begin{aligned}&\Leftrightarrow\frac{73x}{(12+16+9)}\times9=\text{ Rs. }65700\\ &\Leftrightarrow\frac{657x}{37}=\text{ Rs. }65700\\ &\Leftrightarrow x=\text{ Rs. }\frac{65700\times37}{657}\\ &\Leftrightarrow x=\text{ Rs. }3700\\ &\text{ Hence, required profit }\\ &=100x\\ &=100\times3700\\ &=\text{ Rs. }370000\end{aligned}