Races Question Answers

Races - Quant/Math - CAT 2008

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)

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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 =  40/5= 8m/sec.

Running at 8 m/sec B will take 1000/8 = 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 = 1000/100 = 10 m/sec.