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A, B and C invested their capitals in the ratio 3 : 4 : 6. However their share of profit are equal. The duration of their investments must be in the ratio ?

A. 4 : 3 : 2 B. 6 : 4 : 3 C. 3 : 4 : 6 D. 1 : 1 : 1 Answer: Option A
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Solution(By Apex Team)

Let their investments be Rs. 3x for p months Rs. 4x for q months and Rs. 6x for r months respectively Then, $\begin{array}{l} 3 x p: 4 x q: 6 x r=1: 1: 1 \\ \Rightarrow 3 p: 4 q: 6 r=1: 1: 1 \\ \text { So, } 3 p=4 q \\ \Leftrightarrow q=\frac{3 p}{4} \\ \text { And, } 4 q=6 r \end{array}$ $\begin{aligned}&\Leftrightarrow r=\frac{2q}{3}=\left(\frac{2}{3}\times\frac{3}{4}p\right)=\frac{p}{2}\\ &\therefore p:q:r\\ &=p:\frac{3p}{4}:\frac{p}{2}\\ &=4:3:2\end{aligned}$

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