Quantitative Aptitude :: Races and Games - Discussion

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Explanation:
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.