CAT Exam Model Paper 1 with solutions for free online practice

Question : 77 of 100

Marks: +1, -0

A train with 120 wagons crosses Arjun who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the Arjun (he is riding on the horse) before it starts overtaking Srikrishna (who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (inseconds) after the train has crossed the Srikrishna do the Arjun meets to Srikrishna?

3560 sec
3600 sec
3576 sec
can’t be determined

Validate

Solution:

(c) Let the length of the train be L metres and speeds of the train, Arjun and Srikrishna be R, A and K respectively, then

{ L }/{ R - A } = 36\;\;\;\;\;\;\;\;\;\;\;

..(i)
and

{ L } /{ ( R + K ) } = 24\;\;\;\;\;\;\;\;\;\;\;

...(ii)
From eq. (i) and (ii)
3(R − A)= 2(R + K) ⇒ R = 3A + 2K
In 30 minutes (i.e., 1800 seconds), the train covers 1800R (distance) but Arjun also covers 1800A (distance) in the same time.
Therefore distance between Arjun and Srikrishna, when the train has just crossed Srikrishna = 1800(R − A)−24 (A + K)
∴ Time required =

{1800(\R − \A)−24 (\A + \K)}/(\A+\K)

= 3600 − 24 = 3576 s (Since R = 3A + 2K)

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