Two trains starting at the same time from two stations 200 km apart and going…
2023
Two trains starting at the same time from two stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . What is the ratio of their speeds ?
- A.
7:3
- B.
9:4
- C.
11:9
- D.
12:5
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Answer: 11:9
Quick method: One train covers 110 km before meeting, so the other covers 200 − 110 = 90 km in the same time. Speeds are proportional to distances covered in the same time, so ratio = 110:90 = 11:9.
Algebraic method:
Let the speeds of the two trains be x km/h and y km/h.
They meet when (x + y) × t = 200, so the meeting time t = 200/(x + y).
Distance first train covers = x × t = x × 200/(x + y) = 110.
Distance second train covers = y × t = y × 200/(x + y) = 90.
Divide the two equations to get x/y = 110/90 = 11/9, so the speed ratio is 11:9.