In a 100 M race, if A gives B a start of 20 meters, then A wins the race by 5 seconds. Alternatively, if A gives B a start of 40 meters the race ends in a dead heat. How long does A take to run 200 M?
Let us consider A covers 100 m in t sec.
Speed of A = $$\ \frac{100}{t}$$
Since A gave B a headstart of 20m, B covers 80m in (t+5) sec (Given)
Speed of B = $$\ \frac{80}{t+5}$$
If A gives head start of 40m to B, then the time taken by A to cover 100m is the same as the time taken by B to cover 60m
$$\ \frac{100}{\ \frac{\ 100}{t}}$$ = $$\ \frac{60}{\ \frac{\ 80}{t+5}}$$
n solving for t, we get
t = 15 sec
Speed of A = $$\ \frac{100}{15}$$ m/sec
Time taken by A to cover 200m(x) =
200=time * $$\ \frac{100}{15}$$
x = 30 sec
C is the correct answer.
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