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Two trains of which one is 50 metres longer than the other are running in opposite directions and cross each other in 10 seconds. If they be running in the same direction then faster train would have passed the other train in 1 minute 30 seconds. The speed of faster train is 90 km per hr. Find the speed of other train.
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- 25 m/sec.
- 20 m/sec.
- 30 m/sec.
- 35 m/sec.
Correct Option: B
Let the length of trains be x m and (x + 50)m and the speed of other train be y m per sec.
The speed of the first train = 90 km per hr.
| = 90 × | = 25 m per sec. | |
| 18 |
Case : I Opposite direction,
Their relative speed = (y + 25)m per sec.
Distance covered = x + x + 50 = 2x + 50 metres
| ∴ Time taken = | = 10 | |
| y + 25 |
⇒ 2x + 50 = 10y + 250 ...(i)
Case II. Direction is Same
Their relative speed = (25 – y) m per sec.
Distance covered = x + x + 50 = 2x + 50m
| ∴ Time taken = | = 90 | |
| 25 − y |
⇒ 2x + 50 = 90 (25 – y) ...(ii)
From equations (i) and (ii)
10y + 250 = 2250 – 90y
⇒ 10y + 90y = 2250 – 250
| ⇒ y = | = 20 | |
| 100 |
Putting y = 20 in equation (i), we have
2x + 50= 10 × 20 + 250 = 450
⇒ 2x = 450 – 50 = 400
| ⇒ x = | = 200 | |
| 2 |
∴ x + 50 = 200 + 50 = 250 metres.
Hence,
The length of the 1st train = 200 metres.
The length of the 2nd train = 250 metres.
The speed of the 2nd train = 20 m per sec.
