###
**A, B and C invested money in the ratio of $\Large\frac{1}{2}: \frac{1}{3}: \frac{1}{5}$ 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 ?**

A. Rs. 20000, Rs. 25000, Rs. 18000
B. Rs. 15500, Rs. 27200, Rs. 20450
C. Rs. 22500, Rs. 6750, Rs. 5400
D. Rs. 10350, Rs. 21540, Rs. 12050
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

Ratio of capital invested by
$\mathrm{A}, \mathrm{B} \text { and } \mathrm{C}=15: 10: 6$
Total capital invested by A in 1 year
$\begin{array}{l}
=15 x \times 4+30 x \times 8 \\
=300 x
\end{array}$
Total capital invested by B in 1 year
$\begin{array}{l}
=10 x \times 6+5 x \times 6 \\
=90 x
\end{array}$
Total capital invested by C in 1 year
$\begin{array}{l}
=6 x \times 12 \\
=72 x
\end{array}$
Ratio of profits:
$\begin{array}{c}A\quad:\quad B:\quad C\\
300x:90x:72x\\
50x:15x:12x\end{array}$
According to the question,
$\begin{aligned}&\Leftrightarrow(50x+15x+12x)=\text{ Rs. }34650\\
&\Leftrightarrow77x=\text{ Rs. }34650\\
&\Leftrightarrow x=\text{ Rs. }\frac{34650}{77}\\
&\Leftrightarrow x=\text{ Rs. }450\end{aligned}$
$\begin{aligned}\text{ Profit of }\mathrm{A}&=\text{ Rs. }450\times50\\
&=\text{ Rs. }22500\\
\text{ Profit of }\mathrm{B}&=\text{ Rs. }450\times15\\
&=\text{ Rs. }6750\\
\text{ Profit of }\mathrm{C}&=\text{ Rs. }450\times12\\
&=\text{ Rs. }5400\end{aligned}$

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