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1.  Rajdhani Express leaves Delhi for Jaipur at a speed of 120 km/h. After 90 minutes, another train, Delhi Express leaves Jaipur for Delhi at a speed of 100 km/h. When the two trains cross each other which train is closer to Jaipur?

Dear Smaran,

Hope the following may help you:

Assuming that, the two trains A and B are travelling in opposite directions.

Speed of train A travelling from Delhi to Jaipur = 120 km/hr

Speed of train B travelling from Jaipur to Delhi = 100 km/hr
Now, it is given that the train B starts after 90 min than that of the train A.
Suppose the train A reaches the point P after 90 minutes.

Distance covered by the train A in 90 minutes = 120 x (90/60) = 120 x (3/2) = 180 km

Let the total distance between Delhi and Jaipur = (x + 180) km

Here x = distance between point P and Jaipur.

After the train A has reached point P, let after t hours both the trains meet at point Q.

As the trains are moving towards each other so the relative velocity of train A with respect to train B = 120 + 100 = 220 km/h

Now, t = x/220 hrs
Now, distance travelled by train A in t hrs = 6x/11 km
Now, distance travelled by train B in t hrs = x − 6x/11 = 5x/11 km
So, when the two trains cross each other, then 
distance travelled by train A =[ 180 + (6x/11)] km
distance travelled by train B = 5x/11 km

Since the train A is travelling towards Jaipur and train B is travelling towards Delhi,
so, it is clear that when the 2 trains meet each other, they are from same distance Jaipur.
After crossing each other, the train A will be closer to Jaipur as it is heading towards Jaipur.
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