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Problems on Trains - Quantitative Aptitude Test Problems and Solutions


  • 1. A 400m long train is running at 72 Kmph. how much time it will take to cross an electric pole? 
A.) 15sec
B.) 20sec
C.) 19sec
D.) 21sec

Answer: Option 'B'

Formula: Distance = Speed × Time
If we convert Kmph in to Mpsec multiply by 5/18,
400 = 72 KmpH × time
400 = 72×5/18 × time
Time = 20Sec

  • 2. A 180m long train is running at 54 Kmph. how much time it will take to cross a platform of 120m long? 
A.) 20sec
B.) 22sec
C.) 19sec
D.) 18sec

Answer: Option 'A'

Formula: D = S × T 
180 = 54 Kmph × Time 
180= 54×5/18 × Time 
Time = 20 Sec 

  • 3. 320m long train is running at 72 Kmph. how much time it will take to cross a platform of 180m long? 
A.) 20sec
B.) 25sec
C.) 30sec
D.) 27sec

Answer: Option 'B'

Total Length = platform Length+ Train Length 
Total Length= 500m 
D = S × T 
500 = 72 × time 
500 = 72 × 5/18 × time 
Time = 25Sec 

  • 4. A 600m long train is running at 90 Kmph. how much time it will take to cross an electric pole? 
A.) 16sec
B.) 20sec
C.) 24sec
D.) 22sec

Answer: Option 'C'

Formula: D = S × T 
600 = 90 Kmph × T 
600 = 90 × 5/18 × T 
Time = 24Sec

  • 5. Two trains 300m and 400m long run at the speeds of 40 kmph and 50kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other? 
A.) 20sec
B.) 25secs
C.) 26sec
D.) 28sec

Answer: Option 'D'

Length of two Trains = 300m + 400m = 700m 
Total Speed= 40 Kmph + 50 Kmph (Opposite Direction)
= 90 Kmph 
Time = Distance/Speed 
Time = 700/ 90 
Time = 28Sec

  • 6. 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: 
A.) 45 m
B.) 55 m
C.) 50 m
D.) 65 m

Answer: Option 'C'

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x/(y - 5) = 9 and ( x/(y - 10) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.

  • 7. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet? 
A.) 10 a.m.
B.) 11 a.m.
C.) 8 a.m.
D.) 9 a.m.

Answer: Option 'A'

Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.

  • 8. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.) 96 km/hr
B.) 81 km/hr
C.) 51 km/hr
D.) 76 km/hr

Answer: Option 'B'

4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25 m/sec, and
5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train = ( 22.5 x 18/5 ) km/hr = 81 km/hr.

  • 9. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
A.) 27 m
B.) 33 m
C.) 27 7/9 m
D.) 23 4/9 m

Answer: Option 'C'

Relative speed = (40 - 20) km/hr = ( 20 x 5/18 ) m/sec = 50/9 m/sec.
Therefore Length of faster train = ( 50/9 x 5 ) m = 250/9 m = 27 7/9 m.

  • 10. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: 
A.) 2 : 3
B.) 6 : 7
C.) 4 : 3
D.) 9 : 16

Answer: Option 'C'

Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.

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