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.