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Explanation:

Let the total distance be x. So the man travels a distance 3x5 at a speed 3a. Therefore, total time taken to travel this distance = 3x(15a)=x(5a)

time=distancespeed

He then travels a distance 2x5 at a speed 2b. Hence, time taken to travel this distance = 2x(10b)=x(5b). So total time taken in going from A to B = x(5a)+x(5b). Now he travels from B to A and comes back. So total distance travelled = 2x at an average speed 5c.
Hence, time taken to return = 2x(5c).

Since the time taken in both the cases remains the same, we can write x5a+x5b=2x5c

Therefore, 1a+1b=2c.

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