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In a 200m race, if A gives B a start of 25 meters, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 meters the race ends in a dead heat. How long does A take to run 200m?

A.100 seconds
B.112.5 seconds
C.775 seconds
D.87.5 seconds
Answer and Feedback
Answer:C
Feedback:A gives B a start of 25 meters and still wins the race by 10 seconds.
Alternatively, if A gives B a start of 45 meters, then the race ends in a dead heat.
Therefore, the additional 20 meters start given to B compensates for the 10 seconds.i.e., B runs 20 meters in 10 seconds.
Hence, B will take 100 seconds to run 200 meters.
We know that A gives B a start of 45 meters. B will take 22.5 seconds to run this 45 meters as B runs 20 meters 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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