A train travels the distance between A and B at a speed of 60 km/h, while in the opposite direction it comes back at 90 km/h . Another train travels the same distance at the average speed of the first train . The time taken by the second train to travel 432 kms is :

6 h

Let the distance = 180 km  [LCM of 60 and 90]

Average speed =  \(\frac{Total\; Distance}{Total \;time}\)  = \(\frac{2 \;×\; 180}{3 \;+\; 2}\) = 72 km/h

Time taken by second trrain = \(\frac{Distance}{Speed}\) = \(\frac{432}{72}\) = 6 h