A train travelling at the speed of x km/h crossed a 300 m long platform in 30 seconds, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?

96

Length of the platform is 300m = 0.3 km

Speed of a man is 6 km/hr

Let the length of train =  a m

Speed of the train =  b km/hr

According to the question,

b × \(\frac{5}{18}\) = \(\frac{a + 300}{30}\)

b × \(\frac{5}{18}\) = (\(\frac{a}{30}\) + 10)    ----(1)

and

(b - 6) × \(\frac{5}{18}\) = \(\frac{a}{20}\)      ----(2)

on solving both we get

 b = 96

So , The value of b is 96 km/hr