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Races - Quant/Math - CAT 2009
Question 4 the day:
June 2, 2003
The question for the day is from the topic of Races.
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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 |
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(2) |
240 seconds |
| (3) |
160 seconds |
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(4) |
140 seconds |
Correct Answer - (3)
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.
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