Question

If in a 200 m race. A beats B by 31 m and C by 18 m, then in a 350 m race. C will beat B by

• A. 13 m
• B. 35 m
• C. 25 m
• D. 32 m

Answer 1

The Correct Option is C

The task is to determine how far C will beat B in a 350 m race, given the following information from a 200 m race: A beats B by 31 m and C by 18 m. Here's how to solve it:

1. Calculate the speeds of B and C relative to A when A runs 200 m:

Since "A beats B by 31 m," B covers 169 m when A covers 200 m. Thus, B's speed relative to A is 169/200. Similarly, since "A beats C by 18 m," C covers 182 m when A covers 200 m. Thus, C's speed relative to A is 182/200.

2. Calculate the time taken by C and B to run 350 m using their relative speeds:

Let the time taken by A to run 1 m be 1 unit.

- B's time to run 350 m = (350/169) * 200

- C's time to run 350 m = (350/182) * 200

3. Determine the distance C beats B by:

Difference in time = B's time - C's time = ((350/169) - (350/182)) * 200

Simplify this to find the difference in distance for 350 m:

350 * (1/169 - 1/182) * 200

4. Calculate:

350 * (1/169 - 1/182) = 350 * ((182 - 169)/(169 * 182)) = 350 * (13/30758) ≈ 25

Thus, C will beat B by approximately 25 m in a 350 m race.