PROBLEMS ON TRAINS

BASIC CONCEPT

**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.

**FORMULAS**

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) = ()

**EXAMPLE**

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?

A. 54

B. 40

C. 56

D. 42

Answer-C

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?

A. 96

B. 48

C. 50

D. 100

Answer-A

Solution-

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?

A. 15

B. 16.5

C. 15.5

D. 14

Answer-A

Solution-

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?

A. 50

B. 40

C. 44

D. 48

Answer-A

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.

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