Aptitude Problems On Trains

1) What is the speed of the train whose length is 210 metres?

I. The train crosses another train (Howrah Express/12869) of 300 metres length running in opposite direction in 10 seconds.

II. The train crosses another train (Howrah Express/12869) running in the same direction at the speed of 60 km/hr in 30 seconds.

Explanation:

Time taken to cross the train, running in opposite directions = [(l1 + l2)/ (u + v)] sec.

=> 10 = [ (210 + 300)/ (u + v) ]

=>u + v = 51.

Time taken to cross the train, running in same direction = [ (l1 + l2)/(u - v)] sec.

=> 30 =[ (210 + 300)/ (u - 60 x (5/18)) ]

=> u = [ ( 17 +(50/3) ] m/sec.

Thus, u and v can be obtained.

2) What is the length of a running train crossing another 180 metre long train running in the

opposite direction?

I. The relative speed of the two trains was 150 kmph.

II. The trains took 9 seconds to cross each other.

Explanation:

Let the two trains of length a metres and b metres be moving in opposite directions at u m/s

and v m/s.

Time taken to cross each other = [ (a + b)/ (u + v) ] sec.

Now, b = 180, u + v = [ 150 x (5/18) ] m/sec = (125/3 ) m/sec.

=> 9 = [ (a + 180)/ (125/3) ]

=> a = (375 - 180) = 195 m.

3) What is the length of a running train?

I. The train crosses a man in 9 seconds.

II. The train crosses a 240 metre long platform in 24 seconds.

Explanation:

Time taken by train to cross a min = ( Length of train/ Speed of train )=> Speed

= (l/9)....(i)

Time taken by train to cross a platform =[ (Length of train +Length of platform)/ Speed of

train ] =>Speed = (l + 240)/24 ....(ii)

From (i) and (ii), we get l/9 = [ (l + 240)/24 ].

4) What is the speed of the train?

I. The train crosses a signal pole in 18 seconds.

II. The train crosses a platform of equal length in 36 seconds.

III. Length of the train is 330 metres.

Let the speed of the train be x metres/sec.

Time taken to cross a signal pole =( Length of the train / Speed of the train )

Time taken to cross a platform =[ (Length of the train + Length of the Platform)/ Speed of the

train]

Length of train = 330 m.

I and III give, 18 =(330/x) => x =( 330/18) m/sec = ( 55/3 ) m/sec.

II and III give, 36 = [ (2 x 330)/x ] => x = (660/36) m/sec =( 55/3 ) m/sec.

5) What is the speed of the train?

I. The train crosses a tree in 13 seconds.

II. The train crosses a platform of length 250 metres in 27 seconds.

III. The train crosses another train running in the same direction in 32 seconds.

Explanation:

Let the speed of the train be x metres/sec.

Time taken to cross a tree =(Length of the train/ Speed of the train)

Time taken to cross a platform =[ (Length of the train + Length of the Platform)/ Speed of the

train]

I gives, 13 =(l/x) => 13x.

II gives 27 =[ (l + 250)/x ]

=>[ (13x + 250)/x ]= 27

=> x =( 125/7 ) m/sec.