In a 200-m race, if A gives B a head start of 35 m, then A wins the race by 20 sec. Alternatively, if A gives B a head start of 55 m, the race ends in a dead heat. How long does A take to run 200 m?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 145 sec.
Time = Distance / Speed
In the first case:
A runs = 200m , B runs = (200 - 35)m = 165m
Let A take x seconds to run 200 m, then B will take (x+20) seconds for 165m
In the second case:
A runs = 200m, B runs = (200 - 55)m = 145m
Time taken by B to run 145m = time taken by A to run 200m = x s
From the first and second cases, it is clear that for (165 - 145)m = 20 m extra run B takes 20 s extra time.
Thus speed of B = 20m/20s = 1m/s
Therefore, Time taken by A to run 200m = Time taken by B to run 145m = 145/1 = 145 s