a) 4 : 3 : 2
b) 6 : 4 : 3
c) 3 : 4 : 6
d) 1 : 1 : 1
Answer: a
Explanation: Let their investments be Rs. 3x for p months
Rs. 4x for q months and Rs. 6x for r months respectively
$$\eqalign{
& 3xp:4xq:6xr = 1:1:1 \cr
& 3p:4q:6r = 1:1:1 \cr
& {\text{So, }}3p = 4q \cr
& \Leftrightarrow q = \frac{{3p}}{4} \cr
& 4q = 6r \cr
& \Leftrightarrow r = \frac{{2q}}{3} = \left( {\frac{2}{3} \times \frac{3}{4}p} \right) = \frac{p}{2} \cr
& \therefore p:q:r \cr
& = p:\frac{{3p}}{4}:\frac{p}{2} \cr
& = 4:3:2 \cr} $$
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