CAT 2005 Question 2

Instructions

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Question 2

At what time does Shyam overtake Ram?

Solution

Let the time at which Shyam overtakes Ram be t minutes past 10.
So, distance run by both of them is the same till that moment.
(60+t)5 = (15+t)10 => 300 + 5t = 150 + 10t => 5t = 150 => t = 30 min.
So, at 10.30 am, Shyam overtakes Ram



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