Two trains running in opposite direction cross a man standing on the platform in 30 sec and 15 sec respectively and they cross each other in 25 sec. The ratio of their speeds is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2 : 1.
1st train cross the man in 30 seconds
2nd train cross the man in 15 seconds
Relative speed of two trains moving in opposite direction = Speed of 1st train + Speed of 2nd train
Distance = Speed × Time
Let, the speed of the 1st train be x m/sec and that of the 2nd train be y m/sec
When a train crosses a standing man it crosses its length
1st train cross the man in 30 second
⇒ The length of 1st train = 30x meters
2nd train cross the man in 15 seconds
⇒ Length of the 2nd train = 15y meters
Relative speed of two trains is (x + y) m/sec
In 25 seconds they cross each other
⇒ In 25 seconds the cross 25(x + y) meter
Accordingly,
⇒ 25(x + y) = 30x + 15y
⇒ 25x + 25y = 30x + 15y
⇒ 30x - 25x = 25y - 15y
⇒ 5x = 10y
⇒ x/y = 2/1
⇒ x : y = 2 : 1
The ratio of the speed of the two trains is 2 : 1.