A train running at 23.6 km/hr takes 30 seconds to pass a platform. Next, it takes 11 seconds to pass a man walking at 12.4 km/hr in the opposite direction. Find the length of the train.

Given:

A train running at 23.6 km/hr takes 30 seconds to pass a platform. Next, it takes 11 seconds to pass a man walking at 12.4 km/hr in the opposite direction.

Formula used:

Speed of train relative to man = Speed of train + Speed of man

Distance = Speed × Time

Calculation:

Speed of train = 23.6 km/hr = \(\dfrac{23.6 \times 1000}{3600}\) m/s = 6.56 m/s

Speed of man = 12.4 km/hr = \(\dfrac{12.4 \times 1000}{3600}\) m/s = 3.44 m/s

Relative speed = 6.56 + 3.44 = 10 m/s

Time to pass man = 11 seconds

⇒ Length of train = Relative speed × Time

⇒ Length of train = 10 m/s × 11 s

⇒ Length of train = 110 m

∴ The correct answer is 110 m.