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Races - Quant/Math - CAT 2013

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Question 4 the day: May 6, 2002
In a km race, A gives B a start of 20 seconds and beats him by 40m. However, when he gives B a start of 25 seconds they finish in a dead heat. What is A’s speed in m/sec?
(1)12.5 m/sec (2)20 m/sec (3)8 m/sec (4)10 m/sec
Correct Answer - (4)

Solution

A gives B a start of 20 seconds and beats him by 40m in the first race. But when A gives B 25 seconds start, they end in a dead heat.

The extra 5 seconds that A gives B compensates for the 40 m. Therefore, in 5 seconds, B runs 40m. Therefore, speed of B = = 8m/sec.

Running at 8 m/sec B will take = 125 seconds to complete the 1000 meters. As A gives B a start of 25 seconds to finish the race in a dead heat, A will take 125 - 25 = 100 seconds to complete the race.
Therefore, A’s speed = = 10 m/sec.
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