A train passes a stationary pole in 8 seconds. The train also passes a 200 m long bridge in 28 seconds. What is the length of the train?

Question: A train passes a stationary pole in 8 seconds. The train also passes a 200 m long bridge in 28 seconds. What is the length of the train?

Solution:
Given that,
Time to pass a pole = 8 s
Time to pass a 200 m bridge = 28 s

Let the length of the train = L meters
When passing a pole, the train covers distance = L in 8 s
And when passing a bridge, distance = (L + 200) in 28 s

Now,
From pole,
Speed = Distance/Time = L/8 m/s

And,
From bridge,
Speed = Distance/Time = (L + 200)/28 m/s

ATQ,
L/8 = (L + 200)/28
⇒ 28L = 8L + 1600
⇒ 28L - 8L = 1600
⇒ 20L = 1600
⇒ L = 1600/20
∴ L = 80 m

So the length of the train is 80 meters.