Problems on Trains- Aptitude Questions and Answers

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A runner is running at the speed of 12 kmph along side a railway track. He is 200m ahead of the engine of a 160m long train, running at the speed of 48 kmph, in the same direction. How long the train will take to pass the runner?

A)
36 seconds

B)
12 seconds

C)
48 seconds

D)
21 seconds


Correct Answer :

36 seconds


Explanation :

Relative speed when moving in same direction is S1 - S2
Speed of train relative to jogger = (48-12) = 36 kmph = 36*(5/18) = 10 m/sec

When a train of lengths L1 travelling at a speed S crosses a platform/bridge/tunnel of length L2 in time T,
then the equation is given as S = (L1+L2)/T

So,Time taken by train to pass the runner, T =Distance to cover(L1+L2)/Relative speed(S)
=> (200 + 160)/10= 360/10 = 36 Seconds

Time taken by train to pass the runner =36 Seconds

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A train, running at a speed of 36 kmph, takes 60 seconds to cross an electric pole. How much time it will take to cross a platform of length 250 meter?

A)
10 second

B)
80 second

C)
75 second

D)
85 second


Correct Answer :

85 second


Explanation :

Speed of the train = 36 * (5/18) = 10 m/sec.
Length of the train, distance = (Time * Speed ) = (60 * 10 ) = 600 meters

Time taken by the train to cross the platform of length 250 meter
= Time taken by it to cover (600 + 250) m
= 850/10 = 85 sec

If a train, with a speed of 54 km/hr, crossed a pole in 30 second, the length of the train (in meters) is:

A)
1000

B)
900

C)
450

D)
500


Correct Answer :

450


Explanation :

Speed= 54 km/hr =54 *(1000/3600)m/sec = 15 m/sec.
Distance = Time * Speed
Length of the train = (Speed * Time) = 15 * 30= 450 m.

Two trains measuring 120 metre and 180 metre cross each other completely in 10 seconds when running in opposite directions and the faster train takes 30 second to cross the slower train when the two trains are running in the same direction. Find the speed of the faster train?

A)
39 km/h

B)
36 km/h

C)
54 km/h

D)
72 km/h


Correct Answer :

72 km/h


Explanation :

Distance to cover(L1+L2)=>120+180 = 300 meter

Relative speed of the train= 300/10 =30 m/sec

Relative speed when moving in opposite direction is S1 + S2 = 30 m/sec
Relative speed when moving in same direction is S1 - S2= 10 m/sec

So,Time taken by faster train to pass other train,S1=1/2(30+10)
=>20 m/sec
=>20 * (3600/1000) km/h
=>72 km/h

A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?

A)
100m

B)
200m

C)
250m

D)
300m


Correct Answer :

200m


Explanation :

When a train of lengths L travelling at a speed S crosses a pole/pillar/flag post in time T, then the equation is given as S =L/T
Hence, L=10*S m --------------------------(1)

When a train of lengths L1 travelling at a speed S crosses a platform/bridge/tunnel of length L2 in time T, then the equation is given as S = (L1+L2)/T
S = (L+200)/20
20*S=10*S + 200
10*S=200
S=20 m/s

So L= 10*S = 10*20 = 200 m

Two trains running at 36 km/hr and 54 km/hr are running parallel in the opposite direction. If their lengths are 200m and 300m respectively. Then how much time will they take to cross each other?

A)
20 sec

B)
25 sec

C)
30 sec

D)
35 sec


Correct Answer :

20 sec


Explanation :

When two trains of lengths L1 and L2 respectively travelling at the speeds of S1 and D2 respectively cross each other in time T, then the equation is given as S1+S2 = (L1+L2)/T

S1+S2 = 36 km/hr + 54 km/hr = 90 km/hr = 90 km/hr * 5/18 = 25 m/sec
L1+L2 = 200m + 300m = 500 m

Then, S1+S2 = (L1+L2)/T
T = 500/25 sec = 20 sec

A train is running at the speed of 264 Km/hr. If the length of the train is 330m, then how long will it take to cross a platform which is 330m long ?

A)
9 sec

B)
11 sec

C)
12 sec

D)
15 sec


Correct Answer :

9 sec


Explanation :

When a train of lengths L1 travelling at a speed S1 crosses a platform/bridge/tunnel of length L2 in time T, then the equation is given as S1 = (L1+L2)/T
L1+L2 = 330+330 =660 m
S1 = 264 km/hr = (264 * 5/18) m/sec = 220/3 m/sec

Then , S1 = (L1+L2)/T
220/3 = 660 /T
T = 660* 3 / 220 sec = 9 sec

Two train 120 meters and 160 meters in length are running towards each other on parallel lines at the speed of 50 kmph. and 80 kmph. respectively. How long will it take to cross each other after they meet?

A)
7.75 seconds

B)
8.75 seconds

C)
9.75 seconds

D)
10.75 seconds


Correct Answer :

7.75 seconds


Explanation :

Relative speed when moving in opposite direction, S1 + S2 = 50+80 = 130 kmph = 130*(5/18) m/sec
Total distance to cross to clear off each other, L1 + L2 = 120+160 = 280 meters

When a train of lengths L1 travelling at a speed S crosses a platform/bridge/tunnel of length L2 in time T, then the equation is given as S = (L1+L2)/T
So,Time taken cross each other after they meet, T = Distance to cover(L1+L2) / Relative speed(S1 + S2)
=> 280 / (130*(5/18)) = 7.75~ Seconds

An express train runs 900 km at an average speed of 90 km/hour, stopping for 3 minutes at stations after every 100 km. How long it would take to reach its destination?

A)
10 hr 30 min

B)
10 hr 24 min

C)
10 hr 27 min

D)
10 hr


Correct Answer :

10 hr 24 min


Explanation :

Time taken by express train to cover 900 km = 900/90 = 10 hr
Time taken during stoppage= train stop 8 times in the whole journey after every 100 km= 8 *3 = 24 min.
So, total time taken by train including stoppage= 10 hr 24 min.

What is the time taken by a train of length 200 m traveling at a speed of 60 m/s to cross a person traveling at a speed of 36 kmph in the same direction?

A)
4 sec

B)
5 sec

C)
10 sec

D)
11 sec


Correct Answer :

4 sec


Explanation :

Speed of the train=60 m/s
Speed of the man=36 km/h = 36*1000/60*60 m/s= 10 m/s
relative speed=60-10 m/s(as they are moving in same direction)=50 m/s

length of the train=200 m

So,the time taken by a train = length of the train/relative speed
= 200/50
= 4 sec

A train covers a distance of 10 km in 12 min. If its speed is decreased by 10 kmph, then the time taken by the train to cover the same distance will be?

A)
18 min

B)
14 min

C)
15 min

D)
16 min


Correct Answer :

15 min


Explanation :

Time 12 min, Distance = 10 km
Speed of train = 10 / 12 kmpm = 10*60/12 = 50 kmph

New Speed of train after decreased by 10 kmph= 50-10 = 40 kmph
New Speed 40 kmph, Distance = 10 km
Time taken = 10/40 = 1/4 hr = 1/4 × 60 = 15 min

A 200 meter long train runs 55 km / h and takes 55 seconds to cross a bridge. Tell the length of the bridge?

A)
375 m

B)
300 m

C)
350 m

D)
325 m


Correct Answer :

350 m


Explanation :

Let the length of the bridge = X metre
Speed of train = 36 km/hr = 36* 5/18 = 10 m/sec

S=(L1 + L2)/T
10 = 200+X / 55
200+X = 550
X = 550-200 = 350 metre

A 500 ft long train crosses a platform 700 feet in 10 seconds. So what is the speed of that train?

A)
70 ft/s

B)
85 ft/s

C)
100 ft/s

D)
120 ft/s


Correct Answer :

120 ft/s


Explanation :

Speed of the train = Length of (train+platform)/Time = 500+700 / 10 = 120 ft/ sec

A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m. an express train, whose average speed exceeds that of the passenger train by 15 km / hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

A)

4 p.m.


B)

2 a.m.


C)

12 mid-night


D)

6 a.m.



Correct Answer :

6 a.m.


Explanation :

Let the speed of passenger train= x km/hr
Speed of express train = (x + 15) km/hr
Then, As is given

6pm#-----540-----#-----540-----#9pm

(540 / x) - (540 / x + 15) = 3 [6 pm - 9 pm ]
540( 1/x - 1/x + 15) = 3
540( x + 15 - x / x*(x + 15) ) = 3
540*15 = 3x*(x + 15)
x2 + 15X - 2700 = 0
(x + 60)(x - 45) = 0
x = 45 [∵ x ≠ 60]

Time taken by passenger train to reach the meeting point = 540/x = 540/45 = 12 Hrs

Therefore, Both train will meet at (6 pm + 12 Hrs) = 6 a.m.

A 225 m long train is running at a speed of 30 km / hour. How much time does it take to cross a man running at 3 km / hour in the same direction?

A)

40 seconds


B)

30 seconds


C)

25 seconds


D)

15 seconds



Correct Answer :

30 seconds


Explanation :

Relative Speed, in the same direction= Speed of train - Speed of man
=(30 - 3) km/h
=(27*1000/3600) m/s
=(27*5/18)
=15/2 m/s

Time taken to cross the man = Distance/ Relative Speed
= 225 / (15/2)
= 225*2 / 15
= 30 sec

The distance between two cities (M and N) is 569 km. A train starts from city M at 8 am and travel towards city N @ 53 km per hour. Another train starts from city N at 9 am and travel towards city M @ 76 km per hour. At what time will the trains meet?

A)

12:30 pm


B)

1:00 pm


C)

2:30 pm


D)

1:00 pm



Correct Answer :

1:00 pm


Explanation :

Total distance between M and N= 569 km

First train leaves station at 8:00 am and second at 9:00 am. So first train i.e.,
from M to N has covered 53 km distance in 1 hour.

So, distance left between the stations = 569 − 53 = 516 km

trains are travelling in opposite directions. So, relative speed of trains = 53 + 76 = 129 km/h

Now, Time taken to cover 519 km = 519/129= 4 hours

Hence the time, at which both the trains will meet, is 4 hour after second train left i.e., 9:00 am + 4 h = 1:00 pm

A train 100 meters long moving at a speed of 40 km/hr crosses a train 130 meters long coming from the opposite direction in 6 seconds. Find the speed of the second train?

A)

98 km/hr


B)

96 km/hr


C)

94 km/hr


D)

90 km/hr



Correct Answer :

98 km/hr


Explanation :

Time taken to cross= 6 sec = 6/3600 sec = 1/600 hr
Let the speed of the second train be X km/hr
Relative speed = 40 + X km/hr (opposite directions)
Distance covered = 100 + 130 = 230 m = 0.23 km

Time taken to cross= Distance covered/Relative speed
1/600 = 0.23 / 40 + X
40 + X = 138
X = 98 km/hr

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