Problems on Trains
- 1. The distance between two stations P and Q is 145 km. A train with speed of 25 km/h leaves station at 8 : 00 am towards station Q. Another train with speed of 35 km/h leaves station Q at 9:00 am towards station P. Then, at what time both trains meet?
Options- A. 10 : 00 am
- B. 11 : 00 am
- C. 12 : 00 am
- D. 11 : 30 am Discuss
Correct Answer: 11 : 00 am
Explanation:
First train leaves at 8 :00 am and second at 9:00 am.
So, first train i,e from P to Q has covered 25 km distance in 1 h.
So, distance left between the station = 145 - 25 = 120 km
Now, trains are travelling in opposite directions,
So, relative speed = 25 + 35 = 60 km/h
Time taken to cover 120 km = 120/60 = 2h
? The time, at which both the trains will meet, is 2 h after second train left i.e., 9 : 00 am + 2h = 11 : 00 am
- 2. A train, 500 m long passes a standing train in 20 s moving at a speed of 100 km/h. Find the length of the standing train?
Options- A. 50.55 m
- B. 55.56 m
- C. 45.65 m
- D. None of the above Discuss
Correct Answer: 55.56 m
Explanation:
Let x be the length of the standing train
? Speed of the train = (500 + x)/20
? 100 x (5/18) = (500 + x)/20
? 500 + x = (100 x 5 x 20)/18
? 500 + x = 555.56
? x = 555.56 - 500 = 55.56 m
- 3. Two trains travel in opposite direction at 32 km/h and 40 km/h and a man sitting in slower train passes the faster train in 6 s. The length of the faster train is?
Options- A. 120 m
- B. 114 m
- C. 124 m
- D. 136 m Discuss
Correct Answer: 120 m
Explanation:
Relative speed = (32 + 40) = 72 km/h = (72 x 5/18) m/s = 20 m/s
? Length of train = (20 x 6) = 120 m
- 4. Two trains 121 m long and 99 m long are running in opposite direction, first at 40 km/h and the second at 32 km/h. In what time will they completely clear off each other from the moment they meet?
Options- A. 10 s
- B. 11 s
- C. 13 s
- D. 14 s Discuss
Correct Answer: 11 s
Explanation:
Total distance to be traveled = 121 + 99 = 220 m
Relative speed = Sum of speeds = 72 km/h
= 72 x (5/18) = 20 m/s
? Required time = 220/20 = 11s
- 5. A train travailing at a speed of 30 m/s crosses a 600 m long platform in 30 s. Find the length of the train.
Options- A. 120 m
- B. 150 m
- C. 200 m
- D. 300 m Discuss
Correct Answer: 300 m
Explanation:
Let length of the train be x m.
Relative length of the train = (x + 600) m
According to the question,
(x + 600)/30 = 30
? x + 600 = 900
? x = 900 - 600 = 300 m
- 6. A train passes two persons two persons who are walking in the direction opposite to the direction of train at the rate of 10 m/s and 20 m/s respectively in 12 s and 10 s, respectively. Find the length of the train?
Options- A. 500 m
- B. 900 m
- C. 400 m
- D. 600 m Discuss
Correct Answer: 600 m
Explanation:
Let the speed of the train be V
According to the question.
(V + 10) x 12 = (V + 20) x 10
? 6V + 60 = 5V + 100
? x = 100 - 60 = 40 m/s
? Length of the train = (V + 10) x 12
= (40 + 10) x 12 = 600 m
- 7. Two train are running in opposite direction with a speed of 62 kmph and 40 kmph respectively. If the length of one train is 250 meters and they cross each other in 18 seconds, the length of the other train is?
Options- A. 145 metres
- B. 230 metres
- C. 260 metres
- D. Cannot be determined Discuss
Correct Answer: 260 metres
Explanation:
Let the length of another train be L meters.
Their relative speed = (62 + 40) km/hr = 102 x (5/18) = (85/3) m/sec
? 250 + L/(85/3) = 18
? 3(250 + L)/85 = 18
? 250 + L = 510
? L = 260
? Length of another train = 260 meters
- 8. A train travels 100 meters at 70 km hour. A man is running at 10 km per hour in the same direction. What time the train will pass the man?
Options- A. 6 seconds
- B. 62/3 seconds
- C. 7 second
- D. 8 second Discuss
Correct Answer: 6 seconds
Explanation:
Relative speed of the train
= (70 - 10)
= 60 km/hr
= (60 x 5/18)
= 50/3) m/sec.
? Time taken by the train to pass the man
= (100 x 3/50) = 6 sec.
- 9. A train 120 meters long is running at a rate of 54 km/hr. Time taken by the train to cross a tunnel 130 meters long is?
Options- A. 81/3 seconds
- B. 162/3 seconds
- C. 10 seconds
- D. 15 seconds Discuss
Correct Answer: 162/3 seconds
Explanation:
? Speed of the train = 54 x (5/18) m/sec = 15 m/sec
? Time taken by the train to cross the tunnel
= Time taken by it to cover (120 + 130) m
= (250/15) sec
= 162/3
- 10. Two trains are running on parallel lines in the same direction at a speed of 50 km and 30 km per hour respectively. The faster train crosses a man in slower train in 18 seconds. The length of the faster train is?
Options- A. 170 metres
- B. 100 metres
- C. 98 metres
- D. 85 metres Discuss
Correct Answer: 100 metres
Explanation:
Relative speed of both trains
= (50 - 30) = 20 km/hr
= 20 x (5/18) m/sec.
= (50/9) m/sec.
Let the length of the faster train be L
Then, (L x 9)/50 = 18
? L = (18 x 50)/9
= 100 meters
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