A, B and C invested their capitals in the ratio 3 : 4 : 6. However their shares of profit are equal. The durations 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
Answer (as printed): A
Explanation
Let their investments be ₹$3x$ for $p$ months; ₹$4x$ for $q$ months and ₹$6x$ for $r$ months respectively. Then, $3xp:4xq:6xr=1:1:1 \Rightarrow 3p:4q:6r=1:1:1$. So, $3p=4q \Rightarrow q=\frac{3p}{4}$. And, $4q=6r \Rightarrow r=\frac{2q}{3}=\left(\frac{2}{3}\times\frac{3}{4}p\right)=\frac{p}{2}$. $\therefore p:q:r=p:\frac{3p}{4}:\frac{p}{2}=4:3:2$.
Explanation as extracted from the printed page; notation may be imperfect.