Question

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:

• A. 500 m
• B. 200 m
• C. 100 m
• D. 120 m

Answer 1

Answer: (C)

100 m

Answer 2

Let the speeds of A and B be $4x$ and $5x$, respectively. A has a head start of 200 m, so B needs to cover 600 m while A runs 400 m.

The time taken by B to finish the race is:

$t_B = \frac{\text{Distance by B}}{\text{Speed of B}} = \frac{600}{5x}.$

The distance covered by A in this time is:

$\text{Distance by A} = \text{Speed of A} \times \text{Time taken by B} = 4x \times \frac{600}{5x} = 480 \text{ m}.$

Thus, A finishes 480 m while B finishes the race (600 m). The distance by which A wins is:

$600 - 480 = 100 \text{ m}.$

Thus, the distance by which A wins is 100 m.