Question

Two trains running in opposite directions cross a man standing on the platform in 54 sec and 34 sec, respectively and they cross each other in 46 sec. Find the ratio of their speeds.
1. 2 : 5
2. 1 : 2
3. 3 : 2
4. 4 : 1

Answer 1

Correct Answer - Option 3 : 3 : 2

Given:

One train crosses a man on platform in = 54 sec

Another train crosses a man on platform in = 34 sec

Both train crosses each other in = 46 sec

Calculations:

Let the speed of two trains be x and y respectively.

∴ length of 1^st train = 54x

Length of 2^nd train = 34y

According to the question,

(54x + 34y) / (x + y) = 46

⇒ 54x + 34y = 46x + 46y

⇒ 27x + 17y = 23x + 23y

⇒ 4x = 6y

⇒ 2x = 3y

⇒ x/y = 3/2

x : y = 3 : 2

The ratio of their speeds is 3 : 2.