Quantitative Aptitude Notes Part 13( Problems on trains)

Problems on trains

 

There are train based problem based on two object, First is Train and second object is that which is crossed by the train.

 

Some important Facts
If a train moving or cross a pole or man than the first object is train and the second object is pole or man.

  1. If the train moving or cross the platform than the first object is train and second object is platform which is train cross.

 

  1. If a train cross or moving a man who is standing on platform than the train is first object and the second object is man.

 

  1. When a train crossing or moving another train in the same direction or opposite direction than the first object is first train and second object is second train.

Example:
A train having length 250 meters, passes a poll in 5 seconds. How long will it take to cross a bridge 500 meters long?
Answer:
We know the speed of train = 250 meters  .
(250/ 5) m / sec = 50m / sec
Time taken to cross the bridge = (500 / 50) m / sec = 10m / sec

 

Example:
A super fast train 150m long is running at the speed 90 Km / hr. Find the time taken by it to pass a boy standing  near the railway track.
Answer:
After converting the speed of super fast train Km / hr to m / sec

So, (90 x 5 / 18) m / sec = 25 m / sec.
The super fast train passing a standing boy near the railway track = 150 m.
So, The time taken to cross the standing boy is T = D / S = (150 / 25) sec = 6 sec

Example:
A Rajdhani Express train 160m long and running at speed  72 Km / h. It crosses a platform which is 240 m long .How much time will it cross a platform.
Answer:
The length of train and platform is 160m + 240m = 400m,

Speed = (72 x 5)/ 18 = 20 m / sec.

Required time to cross a platform is T = D / S, = 400 / 20 = 20 sec.

 

Example:
In what time will a 350 meter long train running at the speed of 90 km / hr cross a pole ?
Answer:
Speed= 90 x 5 / 18 = 25 m / s
Time = 350 / 25 = 14 seconds

Problem on speed taken by train

Example:
A 150 m long train takes 30 seconds to cross a man standing on a platform, The speed of the train is :
Answer:
We know the formula Speed = Distance / Time
So , Distance = 150 m ,  Time = 30 Seconds
Speed = ( 150 / 30 ) m / sec = 5 m / sec .
speed of the train is 5 m / sec .

Example:
A women on holiday travel first 140 km at  75 km / hr and the next 140 km at  75 km / hr . The average speed for 280 km of the tour is
Answer:
women taking total time to travel is = ( 140 / 75 + 140 / 75 ) = 28 / 5 hrs
Average speed = ( 280 x 5 / 28 ) = 50 km / hr.

 

Example:
A train 165 meters long crosses a electric poll in 5 seconds. The speed of the trains in km /hr is-
Answer:
Speed = Distance / Time
So , Distance = 165 m ,  Time = 5 Seconds
Speed = ( 165 / 5 ) m / sec = 33 m / sec .
Convert m / sec into km / hr (18 / 5) km /hr
33 x 18 / 5 = 594 / 5 = 118.8 km / hr
speed of the train is 118.8 km / hr

Example:
A slow Local train whose length is 150 meter long and a bridge length is 550 meter to cross the bridge by local train in 50 sec, Then find the speed of train to crossing a bridge.
Answer:
The length of both train and bridge that is 150 + 550 = 700 meter, and we know the formula of speed = Distance / Time , So 700 / 50 = 14 meter / sec.

Example:
A boy is standing on a railway bridge and which is 150 m long. He found that a train passes the bridge in 40 seconds but the train himself in 10 sec, Find the length of the train and speed.
Answer:
First we find the length of train, the we assume that length of train be L meters.
then, L / 10 = L + 150 / 40 = 40 L = 10L + 1500 ,
so, L = 50 meter. and now speed of train is D / T = 50 / 10 = 5 m / sec . and now convert it into 5 x 18 / 5 = 18 Km / hr.
So speed of train is 18 Km / hr.

Problem on Train running same direction

Example:
A train is 250 meter long is running of speed 65 Km / hr, A man running at 5 Km / hr isame direction in which the train is moving, find the what time will it pass a man .
Answer: If direction is given in the same direction then we subtract it ( 65 – 5 ) = 60 Km /hr.
and now convert it into m / sec using 60 x 5 / 18 = 50 / 3 m / sec.If the train time taken to passing the man who running , that is 50 / 3 m /sec. So we can easily get the distance of m / sec so it cover 250 meter that is = 250 x 3 / 50 = 15 sec
So, the train time taking to cover distance is 15 sec.

 

Example:
Two super fast train 180 meters and 180 meters in length respectively are running in same directions , one at the rate of 58 km and the other at the rate of 50 km an hours . What time will they be completely clear of each other?
Answer:
Two fast trains are running is same direction and their relative speed is = 58 – 50 = 8 km / hours .
8 x 5 / 18 = 20 / 9  m / sec .
Total length of both train is ( 180 + 180 ) = 360 meters .
So , the required time  is = Total length / Relative speed = 180 + 180 / 30 = 360 x 9 / 20 = 162 sec

Problem on train running opposite direction

Example:
Two super fast train 180 meters and 180 meters in length respectively are running in opposite directions , one at the rate of 58 km and the other at the rate of 50 km an hours . What time will they be completely clear of each other from the moment they meet
Answer:
Two fast trains are running is opposite direction and their relative speed is = 58+50 = 108 km / hours .
So the two trains are each other meet at 108 km /hours

108 x 5 / 18 = 30 m / sec

So, the required time is = Total length / Relative speed = 180 + 180 / 30 = 12 sec

Problem on finding length of train or platform

Example:
A Express train is running at speed of 90 Km / hr. It crosses a bridge whose length is twice that of train in 36 seconds. What is the length of bridge in meter?
Answer:
At First we convert the speed into 90 Km / hr = 90 x 5/18 = 25 m /sec.
now here is suppose the train length is x so bridge length is 2x.
according to question
25 = x + 2x / 36
x = 300 m .
length of platform is 300 x 2 = 600 m.
So length of bridge is 600 meter.

 

Example:
A metro rail is running at speed of 90 km / hr . If crosses a platform whose length is twice that of train in 36 seconds. What is the length of platform in meter?
Answer:
Speed = 90 x 5 / 18 = 25 m / s .
25 = x + 2x / 36
x = 300 meter
Length of platform = 300 x 2 = 600 meter.

Example:
A express train passes a tunnel in 21 sec whose length is 130 m long moving with speed of 90Km / hr. what is the length of tunnel ?
Answer:
Let length be the x meters.
We know the conversion of Km/hr to m/sec is = 90 x 5 / 18 = 25 m/sec
25 = 130 + x / 21
130 + x = 25 x 21
x = 525 – 130
x = 395
so length be the 395 meters.

 

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