In a 600 m race, the ratio of the speeds of two participants A and B is 4 : 5. If A has a head start of 200 m, then the distance by which A wins is:

100 m

The correct answer is Option (3) → 100 m

Total distance of race = 600 m

Distance needed to be covered by A = 400 m (∵ 200 m ahead start)

Let speed of A and B be:

$A = 4x$

$B=5x$

(∵ Ratio of speeds is 4 : 5)

Time taken by A to complete 400 m,

$Time=\frac{Distance}{Speed}=\frac{400}{4x}=\frac{100}{x}$

Distance covered by B in same time:

Distance = Speed × Time

$=5x×\frac{100}{x}=500m$

∴ When A finishes race, B has covered 500 m

⇒ A wins by (600 - 500)m = 100 m