A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x ?

Length the length off the traiin be l m.
A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds
So, length = speed $$\times time$$
(l + 200) = 30x
l = 30x - 200 ---(1)
Speed of man = 6 km/hr = 6 $$\times \frac{5}{18} = 5/3 m/sec
Relative speed = x - 5/3
$$\frac{l}{20} = \frac{3x - 5}{3}$$
put the value of l,
$$\frac{30x - 200}{20} = \frac{3x - 5}{3}$$
90x - 600 = 60x - 100
30x = 500
x = 50/3 m/sec = $$\frac{50}{3} \times \frac{18}{5}$$ = 60 km/hr