Question

# Bombay Express left Delhi for Bombay at 14.30 hrs travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?a. 120 kmb. 360 kmc. 480 kmd. 500 km

Hint: Assume the time required for Bombay express for meeting as ‘x’ and then use the concept that both the trains will meet at same distance and same time. Then use the formula of distance as $Distance=speed\times time$ to get the distances of both the trains and then equate these values to get the values to get the value of ‘x’. Put this value of ‘x’ in one of the formulae of distance to get the final answer.

To solve the given question we will write the given data first, therefore,
Speed of Bombay Express = 60 kmph ……………………………………………. (1)
Speed of Rajdhani Express = 80 kmph …………………………………………… (2)
As the Bombay Express is left at 14.30 hrs therefore we will assume that after ‘x’ hrs it will meet the Rajdhani Express. Therefore,
Time required for Bombay Express for meeting = x hrs ………………………………. (3)
As Rajdhani Express is left at 16.30 hrs i.e. two hrs late than Bombay express therefore it should take two hours less to meet the Bombay Express. Therefore,
Time required for Rajdhani Express for meeting = (x – 2) hrs …………………………. (4)
Now, As the two trains are leaving from the same station and they are travelling the same distance therefore when they will meet each other at that time they should have covered the equal distance therefore we can write, at the time of meeting,
Distance covered by Bombay Express = Distance covered by Rajdhani Express …………………… (5)
Now to proceed further in the solution we should know the formula of distance in terms of speed and time which is given below,

Formula:
$Distance=speed\times time$
By using the above formula we can write,
Distance covered by Bombay Express = (Speed of Bombay Express) $\times$(Time required for Bombay Express
for meeting)
If we put the value of equation (1) and equation (3) in the above equation we will get,

Distance covered by Bombay Express = 60 $\times$ x ………………………………………………. (6)
Also we can write,
Distance covered by Rajdhani Express = (Speed of Rajdhani Express) $\times$ (Time required for Rajdhani
Express for meeting)
If we put the values of equation (2) and equation (4) in the above equation we will get,
Distance covered by Rajdhani Express = 80 $\times$ (x – 2) ……………………………………. (7)
If we put the value of equation (6) and equation (7) in equation (5) we will get,
60 $\times$ x = 80 $\times$ (x – 2)
Therefore, 60x = 80x – 160
Therefore, 60x – 80x = - 160
Therefore, - 20x = - 160
Therefore, $x=\dfrac{160}{20}$
Therefore, x = 8 hrs
If we put the above value in equation (6) we will get,
Distance covered by Bombay Express = 60 $\times$ 8
Therefore distance covered by Bombay Express = 480 km.
If we compare the above equation with equation (5) we will get,
Distance covered by Bombay Express = Distance covered by Rajdhani Express = 480 km.
Therefore the two trains will meet 480 km away from the Delhi stations.
Therefore the correct answer is option (c).

Note: There is a chance that you will get confused while taking the time required for Rajdhani express for meeting but do remember that the trains are going to meet at same time and same distance and for that Rajdhani express should take less time as it is leaving late.