Problems on Trains- Aptitude Questions and Answers

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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

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