Problems on Trains
- 1. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options- A. 36
- B. 45
- C. 48
- D. 49 Discuss
Correct Answer: 48
Explanation:
Relative speed = (60+ 90) km/hr
| = | ❨ | 150 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 125 | ❩m/sec. |
| 3 |
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
| Required time = | ❨ | 2000 x | 3 | ❩sec = 48 sec. |
| 125 |
- 2. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options- A. 10
- B. 12
- C. 15
- D. 20 Discuss
Correct Answer: 12
Explanation:
| Speed of the first train = | ❨ | 120 | ❩ | m/sec = 12 m/sec. |
| 10 |
| Speed of the second train = | ❨ | 120 | ❩ | m/sec = 8 m/sec. |
| 15 |
Relative speed = (12 + 8) = 20 m/sec.
| ∴ Required time = | [ | (120 + 120) | ] | sec = 12 sec. |
| 20 |
- 3. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options- A. 66 km/hr
- B. 72 km/hr
- C. 78 km/hr
- D. 81 km/hr Discuss
Correct Answer: 81 km/hr
Explanation:
| 4.5 km/hr = | ❨ | 4.5 x | 5 | ❩ | m/sec = | 5 | m/sec = 1.25 m/sec, and |
| 18 | 4 |
| 5.4 km/hr = | ❨ | 5.4 x | 5 | ❩ | m/sec = | 3 | m/sec = 1.5 m/sec. |
| 18 | 2 |
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
⟹ 8.4x - 10.5 = 8.5x - 12.75
⟹ 0.1x = 2.25
⟹ x = 22.5
| ∴ Speed of the train = | ❨ | 22.5 x | 18 | ❩ | km/hr = 81 km/hr. |
| 5 |
- 4. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec Discuss
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
- 5. Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options- A. 2 : 3
- B. 4 : 3
- C. 6 : 7
- D. 9 : 16 Discuss
Correct Answer: 4 : 3
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
- 6. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options- A. 36
- B. 45
- C. 48
- D. 49 Discuss
Correct Answer: 48
Explanation:
Relative speed = (60+ 90) km/hr
| = | ❨ | 150 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 125 | ❩m/sec. |
| 3 |
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
| Required time = | ❨ | 2000 x | 3 | ❩sec = 48 sec. |
| 125 |
- 7. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Options- A. 30 km/hr
- B. 45 km/hr
- C. 60 km/hr
- D. 75 km/hr Discuss
Correct Answer: 60 km/hr
Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
| ∴ | (100 + 100) | = 3x |
| 8 |
⟹ 24x = 200
| ⟹ x = | 25 | . |
| 3 |
| So, speed of the faster train = | 50 | m/sec |
| 3 |
| = | ❨ | 50 | x | 18 | ❩km/hr |
| 3 | 5 |
= 60 km/hr.
- 8. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options- A. 9
- B. 9.6
- C. 10
- D. 10.8 Discuss
Correct Answer: 10.8
Explanation:
| Relative speed = (60 + 40) km/hr = | ❨ | 100 x | 5 | ❩m/sec | = | ❨ | 250 | ❩m/sec. |
| 18 | 9 |
Distance covered in crossing each other = (140 + 160) m = 300 m.
| Required time = | ❨ | 300 x | 9 | ❩sec | = | 54 | sec = 10.8 sec. |
| 250 | 5 |
- 9. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options- A. 9 a.m.
- B. 10 a.m.
- C. 10.30 a.m.
- D. 11 a.m. Discuss
Correct Answer: 10 a.m.
Explanation:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
∴ 20x + 25(x - 1) = 110
⟹ 45x = 135
⟹ x = 3.
So, they meet at 10 a.m.
- 10. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options- A. 320 m
- B. 350 m
- C. 650 m
- D. Data inadequate Discuss
Correct Answer: 350 m
Explanation:
| Speed = | ❨ | 300 | ❩ | m/sec = | 50 | m/sec. |
| 18 | 3 |
Let the length of the platform be x metres.
| Then, | ❨ | x + 300 | ❩ | = | 50 |
| 39 | 3 |
⟹ 3(x + 300) = 1950
⟹ x = 350 m.
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