PROBLEMS ON TRAINS (QUANTITATIVE APTITUDE )PART-2

PROBLEMS ON TRAINS (QUANTITATIVE APTITUDE )PART-2 1. A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
A. 190 metres	B. 160 metres
C. 200 metres	D. 120 metres

Here is the answer and explanation

Answer : Option C

Explanation :

Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s

Time taken to cross, t = 18 s

Distance Covered, d = vt = (400/36)× 18 = 200 m

Distance covered is equal to the length of the train = 200 m

2. A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
A. 270 m	B. 245 m
C. 235 m	D. 220 m

Here is the answer and explanation

Answer : Option B

Explanation :

Assume the length of the bridge = x meter

Total distance covered = 130+x meter

total time taken = 30s

speed = Total distance covered /total time taken = (130+x)/30 m/s

=> 45 × (10/36) = (130+x)/30

=> 45 × 10 × 30 /36 = 130+x

=> 45 × 10 × 10 / 12 = 130+x

=> 15 × 10 × 10 / 4 = 130+x

=> 15 × 25 = 130+x = 375

=> x = 375-130 =245

3. A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
A. 182 km/hr	B. 180 km/hr
C. 152 km/hr	D. 169 km/hr

Here is the answer and explanation

Answer : Option A

Explanation :

Length of the train, l = 150m

Speed of the man , Vm= 2 km/hr

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr

Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)

=> 180 = Vt - 2

=> Vt = 180 + 2 = 182 km/hr

4. A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?
A. 120 sec	B. 99 s
C. 89 s	D. 80 s

Here is the answer and explanation

Answer : Option C

Explanation :

v = 240/24 (where v is the speed of the train) = 10 m/s

t = (240+650)/10 = 89 seconds

5. A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
A. 38 sec	B. 35 s
C. 44 sec	D. 40 s

Here is the answer and explanation

Answer : Option D

Explanation :

Speed = 45 km/hr = 45×(10/36) m/s

= 150/12 = 50/4 = 25/2 m/s

Total distance = length of the train + length of the platform

= 360 + 140 = 500 meter

Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds

6. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
A. Insufficient data	B. 3 : 1
C. 1 : 3	D. 3 : 2

Here is the answer and explanation

Answer : Option D

Explanation :

Let the speed of the trains be x and y respectively

length of train1 = 27x

length of train2 = 17y


Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x+y) = 23

=> (27x + 17 y)/ = 23(x+y)

=> 4x = 6y

=> x/y = 6/4 = 3/2

7. A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
A. 46	B. 36
C. 18	D. 22

Here is the answer and explanation

Answer : Option B

Explanation :

Distance to be covered = 240+ 120 = 360 m

Relative speed = 36 km/hr = 36×10/36 = 10 m/s

Time = distance/speed = 360/10 = 36 seconds

8. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
A. 88	B. 70
C. 62	D. 50

Here is the answer and explanation

Answer : Option D

Explanation :

Assume the length of each train = x

Total distance covered for overtaking the slower train = x+x = 2x

Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s

Time = 36 seconds

2x/ (100/36) = 36

=> (2x × 36 )/100 = 36

=> x = 50 meter

9. Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
A. 10.8 s	B. 12 s
C. 9.8 s	D. 8 s

Here is the answer and explanation

Answer : Option A

Explanation :

Distance = 140+160 = 300 m

Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s

Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s

10. Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
A. 56	B. 48
C. 47	D. 26

Here is the answer and explanation

Answer : Option B

Explanation :

Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)

Total distance = 1.1+.9 = 2km

Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds

11. A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
A. None of these	B. 280 meter
C. 240 meter	D. 200 meter

Here is the answer and explanation

Answer : Option C

Explanation :

Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s

Length of the train = speed × time taken to cross the man = 15×20 = 300 m

Let the length of the platform = L

Time taken to cross the platform = (300+L)/15

=> (300+L)/15 = 36

=> 300+L = 15×36 = 540

=> L = 540-300 = 240 meter

12. A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A. 79.2 km/hr	B. 69 km/hr
C. 74 km/hr	D. 61 km/hr

Here is the answer and explanation

Answer : Option A

Explanation :

Let x is the length of the train and v is the speed

Time taken to move the post = 8 s

=> x/v = 8

=> x = 8v --- (1)


Time taken to cross the platform 264 m long = 20 s

(x+264)/v = 20

=> x + 264 = 20v ---(2)


Substituting equation 1 in equation 2, we get

8v +264 = 20v

=> v = 264/12 = 22 m/s

= 22×36/10 km/hr = 79.2 km/hr

13. Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
A. 10	B. 25
C. 12	D. 20

Here is the answer and explanation

Answer : Option C

Explanation :

speed of train1 = 120/10 = 12 m/s

speed of train2 = 120/15 = 8 m/s

if they travel in opposite direction, relative speed = 12+8 = 20 m/s

distance covered = 120+120 = 240 m

time = distance/speed = 240/20 = 12 s

14. Two trains, one from P to Q and the other from Q to P, 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. 2 :1
C. 4 : 3	D. 3 : 2

Here is the answer and explanation

Answer : Option C

Explanation :

Ratio of their speeds = Speed of first train : Speed of second train

= 16−−√9√

= 4:3

15. A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
A. 3 min	B. 4.2 min
C. 3.4 min	D. 5.5 min

Here is the answer and explanation

Answer : Option A

Explanation :

Total distance = 3 ½ + ¼ = 7/2 + ¼ = 15/4 miles

Speed = 75 mph

Time = distance/speed = (15/4) / 75 hr = 1/20 hr = 60/20 minutes = 3 minutes

16. A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
A. 270 m	B. 210 m
C. 340 m	D. 130 m

Here is the answer and explanation

Answer : Option A

Explanation :

Speed= 72 kmph = 72×10/36 = 20 m/s

Distance covered = 250+ x where x is the length of the train

Time = 26 s

(250+x)/26 = 20

250+x = 26×20 = 520 m

x = 520-250 = 270 m

17. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
A. 62 m	B. 54 m
C. 50 m	D. 55 m

Here is the answer and explanation

Answer : Option C

Explanation :

Let x is the length of the train in meter and v is its speed in kmph

x/9 = ( v-2)(10/36) ---(1)

x/10 =( v-4) (10/36) --- (2)


Dividing equation 1 with equation 2

10/9 = (v-2)/(v-4)

=> 10v - 40 = 9v - 18

=> v = 22

Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m

18. A train is traveling at 48 kmph . It crosses another train having half of its length , traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform?
A. 500 m	B. 360 m
C. 480 m	D. 400 m

Here is the answer and explanation

Answer : Option D

Explanation :

Speed of train1 = 48 kmph

Let the length of train1 = 2x meter

Speed of train2 = 42 kmph

Length of train 2 = x meter (because it is half of train1's length)

Distance = 2x + x = 3x

Relative speed= 48+42 = 90 kmph = 90×10/36 m/s = 25 m/s

Time = 12 s

Distance/time = speed => 3x/12 = 25

=> x = 25×12/3 = 100 meter

Length of the first train = 2x = 200 meter


Time taken to cross the platform= 45 s

Speed of train1 = 48 kmph = 480/36 = 40/3 m/s

Distance = 200 + y where y is the length of the platform

=> 200 + y = 45×40/3 = 600

=> y = 400 meter

19. A train having a length of 270 meter is running at the speed of 120 kmph . It crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
A. 320 m	B. 190 m
C. 210 m	D. 230 m

Here is the answer and explanation

Answer : Option D

Explanation :

Relative speed = 120+80 = 200 kmph = 200×10/36 m/s = 500/9 m/s

time = 9s

Total distance covered = 270 + x where x is the length of other train

(270+x)/9 = 500/9

=> 270+x = 500

=> x = 500-270 = 230 meter

20. Two trains, each 100 m long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is
A. 75 km/hr	B. 60 km/hr
C. 35 km/hr	D. 70 km/hr

Here is the answer and explanation

Answer : Option B

Explanation :

Total distance covered = 100+100 = 200 m

Time = 8 s

let speed of slower train is v . Then the speed of the faster train is 2v

(Since one is moving twice as fast the other)

Relative speed = v + 2v = 3v

3v = 200/8 m/s = 25 m/s

=> v = 25/3 m/s

Speed of the faster train = 2v = 50/3 m/s = (50/3)×(36/10) km/hr = 5×36/3 = 5×12 = 60 km/hr

21. Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
A. 10.30 a.m	B. 10 a.m.
C. 9.10 a.m.	D. 11 a.m.

Here is the answer and explanation

Answer : Option B

Explanation :

Assume both trains meet after x hours after 7 am

Distance covered by train starting from P in x hours = 20x km

Distance covered by train starting from Q in (x-1) hours = 25(x-1)

Total distance = 110

=> 20x + 25(x-1) = 110

=> 45x = 135

=> x= 3

Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

22. A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other 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. 81 km/hr	B. 88 km/hr
C. 62 km/hr	D. 46 km/hr

Here is the answer and explanation

Answer : Option A

Explanation :

Let x is the length of the train in meter and y is its speed in kmph


x/8.4 = (y-4.5)(10/36) ---(1)

x/8.5 = (y-5.4)(10/36) ---(2)

Dividing 1 by 2

8.5/8.4 = (y-4.5)/ (y-5.4)

=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4

.1y = 8.5×5.4 - 8.4×4.5

=> .1y = 45.9-37.8 = 8.1

=> y = 81 km/hr

23. A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
A. 10 sec	B. 8 sec
C. 6 sec	D. 4 sec

Here is the answer and explanation

Answer : Option C

Explanation :

Distance = 110 m

Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)

= 66×10/36 mps = 110/6 mps

Time = distance/speed = 110/(110/6) = 6 s

24. A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
A. 150 m	B. 350 m
C. 420 m	D. 600 m

25. A train crosses a post in 15 seconds and a platform 100 m long in 25 seconds. Its length is
A. 150 m	B. 300 m
C. 400 m	D. 180 m

Here is the answer and explanation

Answer : Option A

Explanation :

Assume x is the length of the train and v is the speed

x/v = 15 => v = x/15

(x+100)/v = 25 => v = (x+100)/25

Ie, x/15 = (x+100)/25

=> 5x = 3x+ 300

=> x = 300/2 = 150

26. A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
A. 440 m	B. 500 m
C. 260 m	D. 430 m

Here is the answer and explanation

Answer : Option B

Explanation :

Distance = 800+x meter where x is the length of the tunnel

Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s

Distance/time = speed

(800+x)/60 = 65/3

=> 800+x = 20×65 = 1300

=> x = 1300 - 800 = 500 meter

27. Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
A. 50 sec	B. 58 sec
C. 24 sec	D. 22 sec

Here is the answer and explanation

Answer : Option C

Explanation :

Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s

We are calculating the time taken by the slower train to pass the driver of the faster one

.Hence the distance = length of the smaller train = 500 m

Time = distance/speed = 500/(125/6) = 24 s

28. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. If the fast train completely passes a man sitting in the slower train in 5 seconds, the length of the fast train is :
A. 19 m	B. 2779 m
C. 1329 m	D. 33 m

Here is the answer and explanation

Answer : Option B

Explanation :

Relative speed = 40-20 = 20 km/hr = 200/36 m/s = 100/18 m/s

Time = 5 s

Distance = speed × time = (100/18) × 5 = 500/18 m = 250/9 = 2779 m = length of the fast train

29. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
A. 42	B. 36
C. 28	D. 20

Here is the answer and explanation

Answer : Option B

Explanation :

Distance covered = 120+120 = 240 m

Time = 12 s

Let the speed of each train = v. Then relative speed = v+v = 2v

2v = distance/time = 240/12 = 20 m/s

Speed of each train = v = 20/2 = 10 m/s

= 10×36/10 km/hr = 36 km/hr

30. A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train?
A. 82 kmph	B. 76 kmph
C. 44 kmph	D. 58 kmph

Here is the answer and explanation

Answer : Option A

Explanation :

Total distance = 108+112 = 220 m

Time = 6s

Relative speed = distance/time = 220/6 m/s = 110/3 m/s

= (110/3) × (18/5) km/hr = 132 km/hr

=> 50 + speed of second train = 132 km/hr

=> Speed of second train = 132-50 = 82 km/hr

31. How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
A. 42	B. 50
C. 30	D. 28

Here is the answer and explanation

Answer : Option C

Explanation :

Distance = 500m

Speed = 63 -3 km/hr = 60 km/hr = 600/36 m/s = 50/3 m/s

Time taken = distance/speed = 500/(50/3) = 30 s

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