Races Question Answers

Races - Quant/Math - CAT 2008

Question 4 the day:June 2, 2003

The question for the day is from the topic of Races.

P can give Q a start of 20 seconds in a kilometer race. P can give R a start of 200 meters in the same kilometer race. And Q can give R a start of 20 seconds in the same kilometer race. How long does P take to run the kilometer?

(1)	200 seconds			(2)	240 seconds
(3)	160 seconds			(4)	140 seconds

Correct Answer - (3)

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Solution:

P can give Q a start of 20 seconds in a kilometer race. So, if Q takes 'x' seconds to run a kilometer, then P will take x � 20 seconds to run the kilometer.

Q can give R a start of 20 seconds in a kilometer race. So, if R takes 'y' seconds to run a kilometer, then Q will take y � 20 seconds to run the kilometer.

We know Q takes x seconds to run a kilometer
Therefore, x = y � 20

Therefore, P will take x � 20 = y � 20 � 20 = y � 40 seconds to run a kilometer.

i.e. P can give R a start of 40 seconds in a kilometer race, as R takes y seconds to run a kilometer and P takes only y � 40 seconds to run the kilometer.

We also know that P can give R a start 200 meters in a km race.
This essentially means that R runs 200 meters in 40 seconds.
Therefore, R will take 200 seconds to run a km.

If R takes 200 seconds to run a km, then P will take 200 � 40 = 160 seconds to run a km.