Question

Two trains start at the same time, one from A to B and the other from B to A. They take \(6\dfrac{1}{4}\) hours and 9 hours to reach B and A respectively, after crossing each other on the way. If the speed of the train starting from A is 72 km/h, then what is the speed (in km/h) of the second train?
1. 60
2. 64
3. 54
4. 56

Answer 1

Correct Answer - Option 1 : 60

Given:

Time taken by the train starting from A to reach B, after crossing = \(6\dfrac{1}{4}\) hours = 25/4 hours

Time taken by the train starting from B to reach A, after crossing = 9 hours

Speed of the train starting from A = 72 km/h

Concept used:

If two trains P and Q start at the same time from two points A and B towards each other and after crossing, they take "a" and "b" hours in reaching B and A respectively. Then

P's speed ∶ Q's speed = √b ∶ √a

Calculation:

Let the speed of the train starting from B = v km/h

\(\frac{v}{{72}} = \;\sqrt {\frac{{\left( {\frac{25}{4}} \right)}}{{\ 9}}} \)

⇒ \(\frac{v}{{72}} = \;\sqrt {\frac{25}{36}} \)

⇒ v/72 = 5/6

⇒ v = 60 km/h

∴ The speed of the train starting from B is 60 km/h.