Races - Quant/Math - CAT 2009

Question 4 the day: August 07, 2002
The question for the day is from the topic Races.

A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec?

(1)

8 seconds

(2)

10 seconds

(3)

16.67 seconds

(4)

12.5 seconds

Solution:

A gives B a start of 10 metres in a 100 metre race. This means that when A runs 100 metres, B runs only 90 metres.

Despite that start, A beats B by 1.25 seconds.
As A is running at the speed of 10 m/sec, he will take 10 seconds to complete the 100 metre race. And B takes 10 + 1.25 = 11.25 seconds to cover 90 metres.

Therefore, the speed at which B is running = = 8 m/sec.
Running at 8 m/sec, B will take = 12.5 seconds to complete the 100 metre race.
Hence the correct answer is (4).