Problems on Trains
- 1. A 150 m long train crosses another 210 m long train running in the opposite direction in 10.8 seconds. If the shorter train crosses a pole in 12 seconds, what is the speed of longer train ?
Options- A. 75 kmph
- B. 80 kmph
- C. 54 kmph
- D. 45 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 75 kmph
Explanation:
Total distance = 150 + 210 = 360 mts
Time taken to cross each other when moving in opposite direction = 10.8 sec
Relative speed of trains = (350/10.8) x 18/5 = 3600/30 = 120 kmph
Speed of shorter train = (150/12) x 18/5 = 45 kmph
Hence, speed of longer train = 120 - 45 = 75 kmph.
- 2. An express train takes 4 seconds to enter tunnel which is 1 km long. If it is traveling at 108 km an hour, how long will it take to pass completely through the tunnel ?
Options- A. 33 sec
- B. 37.33 sec
- C. 36.43 sec
- D. 32 sec Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 37.33 sec
Explanation:
Speed = 108 km/hr
enter a tunnel,, means that the train covers a distance equal to its own length
so (108 x 5/18) = x/4 where x= length of train
hence x = 120 mtrs
to pass completely train has to travel a distance = (x + tunnel length) that is 1120 mtrs.
so (1120/t) = (108x5/18)
t = 37.33 sec
- 3. A train for Fathehpur leaves for every 2 hrs 30 min from Agra station. An announcement was made that train left 37 mins ago and next train comes at 17:00hrs. At what time was the announcement made ?
Options- A. 15:07 hrs
- B. 15:20 hrs
- C. 15:05 hrs
- D. 15:00 hrs Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 15:07 hrs
Explanation:
Next train comes at 17:00 hrs.
So, last train will be = 17:00hrs - 2:30hrs
= 14:30hrs
Announcement made after 37 min of the last train.
S0, 14:30hrs + 00:37 min
= 15:07 hrs.
- 4. How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction ?
Options- A. 58 sec
- B. 62 sec
- C. 60 sec
- D. 50 sec Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 50 sec
Explanation:
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 x 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
- 5. A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is ?
Options- A. 400 m
- B. 300 m
- C. 500 m
- D. 600 m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 400 m
Explanation:
Speed = 78 x 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.
- 6. A train covered k km at 40 kmph and another 2k km at 20 kmph. Find the average speed of the train in covering the entire 3k km ?
Options- A. 28 kmph
- B. 24 kmph
- C. 26 kmph
- D. 32 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 24 kmph
Explanation:
Total time taken = k/40 + 2k/20 hours
= 5k/40 = k/8 hours
Average speed = 3k/(k/8) = 24 kmph.
- 7. Two trains, one from Hyderabd to Bangalore and the other from Bangalore to Hyderabad, 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. 3 : 4
- B. 4 : 3
- C. 2 : 3
- D. 3 : 2 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
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
- 8. The length of a brigade which a train 130 m long and traveling at 45kmph can cross in 30 seconds, is
Options- A. 196 mts
- B. 220 mts
- C. 230 mts
- D. 245 mts Also asked in: Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 245 mts
Explanation:
Let the length of the brigade is x mts
Then Distance = 130 + x mts
given speed = 45 kmph = 45 x5/18 m/s
Time = 30 sec
T = D/S
=> 30 = 130+x/(45x5/18)
=> x = 245 mts.
- 9. Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y ?
Options- A. 360 m
- B. 420 m
- C. 460 m
- D. 320 m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 420 m
Explanation:
Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
- 10. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train?
Options- A. 42 kmph
- B. 43 kmph
- C. 40 kmph
- D. 45 kmph Also asked in: TOEFL, GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 40 kmph
Explanation:
We know that, Speed = Distance/time
Let the speed of the train be = x kmph
NORMAL SPEED SPEED 5 KMPH MORE
Distance = 360 Km Distance =360
speed = X Kmph Speed = (x+5)
Time =360/X Time =360/(x+15)
For the same journey if the speed increased 10 kmph more it will take 1 hour less
Time with original speed - time with increased speed = 1
=> (360/x) - (360/x+10) = 1
=> (360(x+5)-360x)/x(x+5) =1
=> 360X + 1800 -360X = X(X+5)
=> X^2 + 5x - 1800 = 0
X = 40 or -45
X cannot be negetive value
X = 40 kmph.
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