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 ?

14 : 3 : 2
26 : 4 : 3
33 : 4 : 6
41 : 1 : 1

Answer:- 1

Explanation:-

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 \\ 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}

$\eqalign{ & 3xp:4xq:6xr = 1:1:1 \cr & {\text{So,}}3p = 4q \cr & \Leftrightarrow q = \frac{{3p}}{4} \cr & {\text{And, }}4q = 6r \cr & \Leftrightarrow r = \frac{{2q}}{3} = \left( {\frac{2}{3} \times \frac{3}{4}p} \right) = \frac{p}{2} \cr & \therefore p:q:r \cr & = p:\frac{{3p}}{4}:\frac{p}{2} \cr & = 4:3:2 \cr}$