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1. 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

Solution:

Let their investments be Rs. 3x for p months
Rs. 4x for q months and Rs. 6x for r months respectively
Then,

\begin{aligned} 3 x p : 4 x q : 6 x r = 1 : 1 : 1 \\ \Rightarrow 3 p : 4 q : 6 r = 1 : 1 : 1 \\ So, 3 p = 4 q \\ \Leftrightarrow q = \frac{3 p}{4} \\ And, 4 q = 6 r \\ \Leftrightarrow r = \frac{2 q}{3} = (\frac{2}{3} \times \frac{3}{4} p) = \frac{p}{2} \\ ∴ p : q : r \\ = p : \frac{3 p}{4} : \frac{p}{2} \\ = 4 : 3 : 2 \end{aligned}

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