Problems on Trains
- 1. Agra and Delhi are 160 km apart. A train leaves Agra for Delhi and at the same time another train leaves Delhi for Agra. Both the trains meet 5 hrs after they start moving. If the train travelling from Agra to Delhi travels 6 km/hr faster than the other train, find the speed of the faster train?
Options- A. 19 kmph
- B. 13 kmph
- C. 7 kmph
- D. 9 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 19 kmph
Explanation:
Let the speed of the slower train = p kmph
ATQ,
Speed of the faster train = (p + 6) kmph
Then,
(p + p + 6) x 5 = 160
10p + 30 = 160
10p = 130
p = 13 kmph
Then, speed of the faster train = p + 6 = 13 + 6 = 19 kmph.
- 2. An Engine length 1000 m moving at 10 m/s. A bird is flying from engine to end with 'x' m/s and coming back at '2x' m/s. Take total time of bird travelling as 187.5 s. Find x and 2x in km/hr ?
Options- A. 21.4 and 42.8
- B. 25.2 and 50.4
- C. 31.4208 and 62.8416
- D. 33.12 and 66.24 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 31.4208 and 62.8416
Explanation:
Birds speeds in mtrs/sec is 'x' and '2x' .
While flying from Engine to end, relative speed = (x+10) m/sec
from end to engine, flying speed = (2x - 10) mtr/sec
so
1000/(x+10) + 1000/(2x-10) = 187.5 secs
solving it, we get
so x = 8.728 m/sec and 2x= 17.456 m/sec
x = 31.4208 km/hr and 2x = 62.8416 km/hr.
- 3. Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is ?
Options- A. 387 kms
- B. 242 kms
- C. 145 kms
- D. 444 kms Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 444 kms
Explanation:
1h ----- 5 kms
? ------ 60 kms
Time = 12 hrs
Relative Speed = 16 + 21 = 37 kmph
T = 12 hrs
D = S x T = 37 x 12 = 444 kms.
- 4. Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions ?
Options- A. 10 sec
- B. 11 sec
- C. 12 sec
- D. 8 sec Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 10 sec
Explanation:
Relative Speed = 60 -40 = 20 x 5/18 = 100/18
Time = 50
Distance = 50 x 100/18 = 2500/9
Relative Speed = 60 + 40 = 100 x 5/18
Time = 2500/9 x 18/500 = 10 sec.
- 5. Two trains of equal length are running on parallel lines in the same direction at 36 km/hr and 26 km/hr. The faster train passes the slower train in 36 sec. The length of each train is ?
Options- A. 28 mts
- B. 54 mts
- C. 24 mts
- D. 50 mts Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 50 mts
Explanation:
Let the length of each train be x mts.
Then, distance covered = 2x mts.
Relative speed = 36 - 26 = 10 km/hr.
= 10 x 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50 mts.
- 6. The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 kmph. Then find the speed of faster train ?
Options- A. 68 kmph
- B. 52 kmph
- C. 76 kmph
- D. 50 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 68 kmph
Explanation:
Let the speed of the faster train be 'X' kmph,
Then their relative speed= X - 48 kmph
To cross slower train by faster train,
Distance need to be cover = (400 + 600)m = 1 km. and
Time required = 180 sec = 180/3600 hr = 1/20 hr.
Time = Distance/Speed
=> 1/20 = 1/(x-48)
X = 68 kmph
- 7. Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a girl sitting at window seat in the slower train in 32 seconds. Find the length of the faster train ?
Options- A. 170 m
- B. 100 m
- C. 270 m
- D. 320 m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 320 m
Explanation:
Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.
Distance covered in 32 sec = 32 x 10 = 320 m.
The length of the faster train = 320 m.
- 8. Train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 20 seconds. The length of train K is three-fourths the length of train L. What is the ratio of the speed of train K to that of train L ?
Options- A. 1 : 3
- B. 2 : 1
- C. 3 : 1
- D. 1 : 2 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 2 : 1
Explanation:
Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.
Let the length of train K be Lk and that of train L be Ll
given that Lk = 3/4 Ll
As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30
Speed of train L = sl = Ll/80
Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40
Ratio of their speeds = sk : sl
= Ll/40 : Ll/80
=> 1/40 : 1/80 = 2 : 1
- 9. A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options- A. 49 kmph
- B. 50 kmph
- C. 51 kmph
- D. 52 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 49 kmph
Explanation:
Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'x' km/hr.
Then, relative speed = (x - 4) km/hr.
x - 4 = 45 => x = 49 km/hr.
- 10. A passenger train is moving at a speed of 120 km/hr. If the length of the train is 101 meters, how long will it take to cross a railway platform 154 meters long ?
Options- A. 6.24 sec
- B. 6.58 sec
- C. 7.325 sec
- D. 7.65 sec Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 7.65 sec
Explanation:
Here total distance = 154 + 101 = 255 mts
Given speed = 120 kmph = 120x5/18 m/sec
Hence, Time = d/s = 255x18/120x5 = 7.65 sec
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