Problems on Trains
- 1. A train running at the speed of 45 kmph took 12 seconds in passing a certain point. Then the length of the train must be?
Options- A. 90 meters
- B. 120 meters
- C. 150 meters
- D. 540 meters Discuss
Correct Answer: 150 meters
Explanation:
? Speed = (45 x 5/18) = (25/2) m/sec
Distance = (Time x Speed) = (12 x 25 / 2 ) meters
= 150 meters
? Length of the train = 150 meters
- 2. A train 75 meters long is running with a speed of 20 km/hr. It will pass a standing man in?
Options- A. 12 seconds
- B. 13.5 seconds
- C. 14 seconds
- D. 15 seconds Discuss
Correct Answer: 13.5 seconds
Explanation:
? Speed of the train = 20 x (5/18) = (50/9) m/sec
? Time taken by the train to pass the man = 75 x (9/50) = 13.5 sec
- 3. Two stations A and B are 110 kms apart on a straight line. One train start from A at 7 a.m. and travels towards B at 20 km per hour speed. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km per hour. At what time will they meet?
Options- A. 9 a.m.
- B. 10 a.m
- C. 11 a.m
- D. None of these Discuss
Correct Answer: 10 a.m
Explanation:
Suppose they meet T hrs after 7 a.m
? Distance covered by A in T hrs = (20 x T) km
Distance covered by B in (T - 1) hrs = 25(T - 1) km
? 20T + 25 (T -1) = 110
? 45 x T = 135
? T = 3 hours
So, they meet at 10 a.m.
- 4. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?
Options- A. 72 meters
- B. 54 meters
- C. 50 meters
- D. 45 meters Discuss
Correct Answer: 50 meters
Explanation:
Let the length of the train be L km and its speed by y km/hr
Then , speed of train relative to first man = (y - 2) km/hr
Speed of train relative to second man = (y - 4) km/hr
? L / (y - 2) = 9 /(60 x 60)
and L / (y - 4) = 10/ (60 x 60)
? 9y - 18 = 3600 x L ...(1)
and 10y - 40 = 36000 x L ... (2)
So, 9y - 18 = 10y - 40
? y = 22
? L/ (22 - 2) = 9/ 3600
? L = (20 x 9) / 3600 = 1/20 km = (1/20) x 1000 = 50 m.
- 5. A train 100 meter long moving at a speed of 50 kmph crosses a train 120 meters long coming from opposite direction in 6 seconds. The speed of second train is?
Options- A. 132 kmph
- B. 82 kmph
- C. 60 kmph
- D. 50 kmph Discuss
Correct Answer: 82 kmph
Explanation:
Let the speed of the second train be y km/hr
Relative speed of both trains = (50 + y) km/hr
Total distance traveled = 100 + 120 = 220 meters = 0.22 km
Time = 6 sec = 6/( 60 x 60) hr.
Speed = distance/time
? 50 + y = (0.22 x 60 x 60)/ 6
? 50 + y = 132
? y = 82
? Speed of the second train = 82 km/hr
- 6. A train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 second. Its length in meters is?
Options- A. 200
- B. 150
- C. 50
- D. Data inadequate Discuss
Correct Answer: 150
Explanation:
Let the length of the train be 'L' meters and its speed be 'v' meters/sec
Then, L/v = 15
? v = L/15 ....(1)
Now, (L + 100)/25 = L/15
? L = 150 m
- 7. Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 1 minute. If the length of the first train is 125 metres, the length of second train is?
Options- A. 125 metres
- B. 150 metres
- C. 200 metres
- D. 175 metres Discuss
Correct Answer: 175 metres
Explanation:
Relative speed of the train = (40 - 22) km/hr = 18 km/hr
Relative speed of the train in m/sec = 18 x (5/18) = 5 m/sec.
Let the length of 2nd train be L meters.
Then, (125 + L) / 5 = 60 sec.
? 125 + L = 300
? L = 175
? Length of second train = 175 meters
- 8. A 150 meter long train crosses a man walking at the speed of 6 kmph in the opposite direction in 6 seconds. The speed of the train in km/hr is?
Options- A. 66
- B. 84
- C. 96
- D. 106 Discuss
Correct Answer: 84
Explanation:
Let the speed of the train be v km/hr
Relative speed of the train = (v + 6) km/hr = [(v + 6) x 5/18] m/sec
? 150/6 = (v + 6) x (5/18)
? 5v + 30 = 450
? v = 84 km/hr
- 9. A train is running at the rate 40 kmph. A man also is going in the same direction parallel to the train at the speed of 25 kmph. If the train crosses the man in 48 sec, the length of the train is?
Options- A. 50 meters
- B. 100 meters
- C. 150 meters
- D. 200 meters Discuss
Correct Answer: 200 meters
Explanation:
? Relative speed of the train = (40 - 25) km/hr = 15 x (5/18) = 25/6 m/sec
? Length of the train = (48 x 25) / 6 = 200 meters .
- 10. A train of length 150 meters takes 10 seconds to pass over another train 100 meters long coming from the opposite direction. If the speed of the first train be 30 kmph, the speed of the second train is?
Options- A. 54 kmph
- B. 60 kmph
- C. 72 kmph
- D. 36 kmph Discuss
Correct Answer: 60 kmph
Explanation:
Relative speed of both trains = (150 + 100)/10 = 25 m/sec = 25 x (18/5) = 90 km/hr
? Speed of second train = (90 - 30) = 60 km/hr .
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.