PROBLEMS ON TRAINS
POINTS TO BE REMEMBER
⦁ Time Taken by Train to cross any point, pole, object or a Platform –
This type of question may be asked where the students have to calculate the time taken by a train to cross a point, pole, object Platform or stationary body.
⦁ Time Taken by two trains to cross each other –
In this type of problem, students may be asked to find out the time taken by two trains to cross each other.
⦁ Train Problems based on Equations –
There could be two cases asked where the question and the candidates will have to form equations based on the condition given in the question.
When a train crosses a single post or pole or man or tree, then the train will move a distance equal to the length of the train.
So time is taken by train to cross =
⦁ When a train crosses a platform or a bridge, the train has to cross the distance equal to the sum of the length of the train and bridge.
So time is taken by train to cross =
⦁ If two trains of length 'x' meters and 'y' meters move in the same direction with speed S1 m/s and S2 m/s resp.
Where S1 > S2 then relative speed = (S1 – S2) m/s and Time is taken by faster
train to cross the slower train =
⦁ If two trains of length 'x' meters and 'y' meters move in opp. direction with speed S1 m/s and S2 m/s resp.
Where S1 > S2 then their relative speed = (S1 + S2) m/s and
Time is taken to cross each other =
⦁ If two trains (or objects) start at the same time from opposite points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = ()
1. A train is running at a speed of 99 km/h. If the train is 565 m long, then what will be the time (in seconds) taken by it to cross a 975 m long tunnel?
Solution-Speed of train = 99 kmph
Length of train = 565 m
Length of tunnel = 975 m
As we know,
According to the question
Hence, Time required by train to cross the tunnel = 56 m
2. If a person travels at a speed of 48 km/h, he will reach his destination on time. He covers two-thirds of his journey in five-sixths of time. At what speed (in km/h) should he travel to cover the remaining distance to reach his destination on time?
Let the total time taken in journey = x hour
We know that:
Distance = time × speed
= (x) × 48
= 48 km
Now, two thirds of his journey covered by him in five – sixths of time
So, remaining distance to be cover = (48x) × = (48x) × = 16x
Remaining time = (x) - =
Therefore, required speed to cover the remaining distance of time = = 96 km/h
3. Trains A and B of lengths 329 m and 296 m, respectively, are running in opposite directions on parallel tracks, at the speeds of 85 km/h and 65 km/h, respectively. In what time in seconds) will they cross each other?
Total distance = 329 + 296 = 625 m
Relative speed = (85+65) km/h = 150 × m/sec = m/sec
Therefore, required time taken by train A and B to cross each other= 15 sec
4. A train starts running at a uniform speed of 60 km/h from station P towards station Q. At the same time another train starts running from station Q towards station P. If the distance between stations P and Q is 275 km and the trains meet in two and a half hours, then what is the speed of the train running towards station P in km/h?
Solution-Let train X starts running at a uniform speed of 60 km/h from station P towards station Q.
At the same time, another train Y starts running at a uniform speed of S km/h from station Q towards station P.
Distance between the stations P and Q = 275 km
Both trains meet in two and a half hours.
If two trains are moving towards each other then net speed will be some of the speeds of two trains.
Hence, Required speed = 50 km/hr.
- Previous Year's Papers for CSIR-NET Exam: Attempt Here
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