A train traveling at the speed of x km/h crossed a 400 m long platform in 36 seconds and overtook a man walking in the same direction at the speed of 5 km/h in 18 seconds. What is the value of x?
Answer & explanation
Correct answer: option 4
Let the length of train = L
Speed of train =x km/hr or x × \(\frac{5}{18}\) m/sec
For platform:
Total distance traveled by train in 36 sec = (L + 400) = {x × \(\frac{5}{18}\)} × 36
L = 10x - 400
For man:
Total distance traveled by train in 18 sec = L
Relative speed = (x - 5) km/hr or (x - 5) × \(\frac{5}{18}\) m/sec
L = {(x - 5) × \(\frac{5}{18}\)} × 18
L = (x - 5) × 5
Length of train is equal in both conditions, so:
(x - 5) × 5 = 10x - 400
5x - 25 = 10x - 400
5x = 375
x = 75 km/h