Problems on Trains
- 1. A 400 m long train takes 36 s to cross a man walking at 20 km/h in the direction opposite to that of the train. What is the speed of the train?
Options- A. 20 km/h
- B. 30 km/h
- C. 15 km/h
- D. 11 km/h Discuss
Correct Answer: 20 km/h
Explanation:
Relative speed of train = 400/36 m/s = 400/36 x (18/5) = 40 km/h
Relative speed of train = Speed of train + Speed of man
? 40 = Speed of train + 20
? Speed of train = 40 - 20 = 20 km/h
- 2. Two trains of lengths 105 m and 90 m, respectively run at the speeds of 45 km/h and 72 km/h, respectively in opposite directions on parallel tracks. Find the time which they take to cross each other?
Options- A. 5 s
- B. 6 s
- C. 7 s
- D. 8 s Discuss
Correct Answer: 6 s
Explanation:
Total length of the train = 105 + 90 = 195 m
Relative speed = 72 + 45 km/h = 117 km/h = 117 x (5/18) = 585/18 m/s
? Required time = (195 x (18/585) s = 6 s
- 3. A 110 m long train is running at a speed of 60 km/h. How many seconds, does it take to cross an another train of length 170 m, which is standing on parallel track?
Options- A. 15.6 s
- B. 16.8 s
- C. 17.2 s
- D. 18 s Discuss
Correct Answer: 16.8 s
Explanation:
Speed = 60 km/h = 60 x (5/18) m/s = 50/3 m/s
Required time = (110 + 170) / (50/3) = (280 x 3)/50 = 16.8 s
- 4. Two train of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes the slower train in 36 s. The length of each trains is?
Options- A. 82 m
- B. 50 m
- C. 80 m
- D. 72 m Discuss
Correct Answer: 50 m
Explanation:
Let the length of each train be L m.
Relative speed = 46 - 36 = 10 km/h = 10 x 5/18 m/s = 25/9 m/s
Sum of length of train / Relative speed of train = Time taken
? 2L/(25/9) = 36
? 2L = (36 x 25)/9 = 100
? L = 50 m.
- 5. Two trains of same length are running in parallel tracks in opposite directions with speeds 65 km/h and 85 km/h respectively. They cross each other in 6 s . The length of each train is?
Options- A. 100 m
- B. 115 m
- C. 125 m
- D. 150 m Discuss
Correct Answer: 125 m
Explanation:
Let length of each train be L m.
Then. (65 + 85 ) x 5/18 = (L + L)/6
? (150 x 5 x 6)/18 = 2L
? 2L = 250
? L = 125 m
- 6. Two train start at the same time from points x and y towards each other and after crossing, they take 9 h and 4 h in reaching points y and x, respectively. Find the ratio of speeds of the 1st train to that of the 2nd train?
Options- A. 2 : 3
- B. 3 : 2
- C. 2 : 5
- D. 5 : 3 Discuss
Correct Answer: 2 : 3
Explanation:
Given that, T1 = 9 h and T 2 = 4 h
According to the formula.
(1st train's speed) : (2nd train's speed) = ?4 : ?9
= 2 : 3
- 7. The ratio between the speeds of two train is 8 : 9 Second train covers 360 km in 4 h. Distance covered by first train in 3 h (in km ) is?
Options- A. 240
- B. 480
- C. 120
- D. 60 Discuss
Correct Answer: 240
Explanation:
Let speed of 1st train be 8S and speed of 2nd train be 9S
According to the question.
Speed of second train = 360/4 = 90 km/h
9S = 90
? S = 10
So, speed of 1st train = 8 x 10 = 80 km/h
? Required distance = 80 x 3 = 240 km
- 8. From station M and N, two trains start moving towards each other at speed 125 km/h and 75 km/h, respectively. When the two trains meet each other, it is founds that one train covers 50 km more than another. Find the distance between M and N.?
Options- A. 190 km
- B. 200 km
- C. 145 km
- D. 225 km Discuss
Correct Answer: 200 km
Explanation:
Let the trains meet after time t at a distance x from station N.
Then another train coming from station M covers a distance of (x + 50)
For station M,
(x + 50) = 125t
? x = 125t - 50 ..(i)
For station N,
x = 75t .....(ii)
From Eqs. (i) and (ii), we get
75t = 125t - 50
? t = 1h
Distance between station M and N = 125 + 75t = 200 x 1 = 200 km
- 9. Excluding stoppages, the speed of a train is 108 km/h and including stoppages, it is 90 km/h. For how many minute does the train stop per hour?
Options- A. 5
- B. 9
- C. 10
- D. 6 Discuss
Correct Answer: 10
Explanation:
Because of stoppages, train covers 18 km less per hour .
? Time taken to cover 18 km = 18/108 = 1/6 h = (1/6) x 60 = 10 min
- 10. Without stoppages, the speed of a train is 150 km/h and with stoppages, it is 100 km/h. How many minutes does the train stop?
Options- A. 20
- B. 15
- C. 25
- D. 45 Discuss
Correct Answer: 20
Explanation:
Because of stoppages, train covers 50 km less per hour.
? Time taken taken to cover 50 km = 50/150 h = (50/150) x 60 = 20 min
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