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