Hi Shubhankar,
2x/5c is the time taken by the man to travel from A to B and from B to A with speed 5c. In the question it is given that this time is equal to the total time taken by the man to travel 3/5th distance at 3a and the remaining at 2b.
Hope you understood. For further clarification feel free to ask.

Please read the question and solution again. He travelled from B and A and back. So total distance is 2x and speed is 5c.

Avoid committing these kind of silly mistakes in CAT as it will hurt your percentile.

Hi Prashant,
It is given that If he goes from B to A and return at a speed 5c in the same time. So basically he is going to B to A and returning back fom A to B at ta speed of 5c. Hence, time taken = $$\dfrac{2x}{5c}$$

Hi Akash,
In the first case, the man is traveling from A to B, so we cannot take the man traveling from B to A as the first case. It is clearly stated in the question that when a man is traveling from A to B for the first 3/5th of the distance, he is traveling at a speed of 2a, and for the rest, that is 2/5th of the distance, he is traveling at 2b. Then, he travels from B to A and returns to B from A, taking the same time as the above case when he travels at a speed of 2c. Using these conditions, we solved the question in solution.
Hope this clears your doubt!