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# Maths : Problems on Train (Solved in Steps)

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

Explanation :

Speed of the train = 40 km/hr
= 40000/3600 m/s
= 400/36 m/s
Time taken to cross = 18 s
Distance Covered = speed× time
= (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

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 thetrain, 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

Explanation :

Length of the train, l = 150m
Speed of the man = 2 km/hr
Relative speed = total distance/time = (150/3) m/s
= (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train – Speed of man (As both are moving in the same direction)
=> 180 = Speed of train – 2
=> Speed of train = 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

Explanation :

speed of the train = 240/24 = 10 m/s
time taken to pass a platform having a length of 650 m
= (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

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

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
ratio of their speeds=3:2

7. 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

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

8. 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

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

9. 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

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

10. 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

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

11. 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

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

12. 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

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

13. A train having a length of 1/4 mile, is travelling 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

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

14. 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

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 mx = 520-250 = 270 m

15. 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

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

16. A train is travelling at 48 kmph . It crosses another train having half of its length, travelling 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

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

17. A train having a length of 270 meters 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

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

18. 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

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

19. 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

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

20. 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

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

21. 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

Explanation :

Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110

22. 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

Explanation :

Length of the train
= distance covered in crossing the post
= speed × time
= speed × 18
ie,300= speed × 18
Speed of the train = 300/18 m/s = 50/3 m/s
Time taken to cross the platform = 39 s
(300+x)/(50/3) = 39 s where x is the length of the platform
300+x = (39 × 50) / 3 = 650 meter
x = 650-300 = 350 meter

23. 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

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

24. 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

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

25. Two trains 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

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

26. Two trains are running in opposite directions at 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

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

27. 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

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

28. 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