A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.

Question: A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.

Solution:
Let the length of the train be x m

Speed equal in both case,
then
x/32 = (x + 420)/62
⇒ 62x = 32x + 420 × 32
⇒ 62x - 32x = 420 × 32
⇒ 30x = 420 × 32
⇒ x = (420 × 32)/30
∴ x = 448 m

∴ Length of train is 448 m.