Answer: Option C
:
C
Approach 1: Conventional Approach :
option (c) time taken to cover AC $=\frac{3x}{5}\times 3a=\frac{x}{5a}$ hr.
Time taken to cover CB $=\frac{x}{5b}$ hr.
Time taken to cover BA and back AB $=\frac{2x}{5c}$
Given $\frac{x}{5a}+\frac{x}{5b}=\frac{2x}{5c}\to \frac{1}{a}+\frac{1}{b}=\frac{2}{c}$
Approach 2:Shortcut using Assumption !
As the questions in terms of variables we can assume values for all the given variables .
Let the distance AB be 5 kms:
The man travels three-fifth of a distance AB at a speed 3a. If we take a=1 we see that he covers a distance of 3 km.The remaining distance of 2 kms is covered in 2b time we get b=1. Also, he goes from B to A and returns at a speed 5c in the same time, we see that c=0.5. Sub these values into the options we find that only (c) fits in. (all the other options get eliminated)