Races - CAT 2007
Question 4 the day:
April 24, 2006
The question for the day is a sample practice problem in races between two people. It is an Arithmetic Topic and the problem provides an understanding of the start given by one person to the other measured in terms of both time and distance.
Question:
In a 200m race, if A gives B a start of 25 metres, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 metres the race ends in a dead heat. How long does A take to run 200m?
- 100 seconds
- 112.5 seconds
- 77.5 seconds
- 87.5 seconds
Correct Answer - 77.5 seconds. Choice (3)
Explanatory Answer
A gives B a start of 25 metres and still wins the race by 10 seconds.
Alternatively, if A gives B a start of 45 metres, then the race ends in a dead heat.
Therefore, the additional 20 metres start given to B compensates for the 10 seconds.
i.e., B runs 20 metres in 10 seconds.
Hence, B will take 100 seconds to run 200 metres.
We know that A gives B a start of 45 metres. B will take 22.5 seconds to run this 45 metres as B runs 20 metres in 10 seconds or at the speed of 2 m/s.
Hence, A will take 22.5 seconds lesser than B or 100 - 22.5 = 77.5 seconds to complete the race.
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