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:
Answer & explanation
Correct answer: option 3
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