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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
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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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