In a 100 m race, runner A can beat B by 25 m and B can beat C by 4 m. In the same 100 m race, by how many metres can A beat C?

Introduction / Context:
This is the same logical pattern as an earlier race problem about three runners. It checks whether you can combine two leads, A over B and B over C, correctly by working with speed ratios rather than just adding distances. The numbers are kept simple to highlight understanding rather than heavy computation.

Given Data / Assumptions:
- When A finishes 100 m, B has covered 75 m. - When B finishes 100 m, C has covered 96 m. - All runners maintain constant speeds during the race. - We must find the distance by which A beats C in the same 100 m race.

Concept / Approach:
We convert the given information into ratios of speeds vA, vB, and vC. From the first statement we get vB relative to vA, and from the second we get vC relative to vB. Multiplying the ratios gives vC relative to vA. Then we find the distance C covers while A runs 100 m and subtract to find the lead of A.

Step-by-Step Solution:
Step 1: From A vs B, vB / vA = 75 / 100 = 3 / 4. Step 2: From B vs C, vC / vB = 96 / 100 = 24 / 25. Step 3: Therefore vC / vA = (vC / vB) * (vB / vA) = (24 / 25) * (3 / 4) = 72 / 100 = 18 / 25. Step 4: When A runs 100 m, time taken is T = 100 / vA. Step 5: In the same time, C runs distance = vC * T = 100 * (vC / vA) = 100 * 18 / 25 = 72 m. Step 6: Lead of A over C = 100 - 72 = 28 m.

Verification / Alternative check:
Assume vA = 25 units. Then vB = 3/4 of 25 = 18.75 units, and vC = 24/25 of vB = 18 units. Time for A to complete 100 m is 100 / 25 = 4 units. In 4 units, C covers 18 * 4 = 72 m. The difference 28 m matches the earlier calculation, confirming the result.

Why Other Options Are Wrong:
- 21 m and 26 m: These are produced when ratios are handled incorrectly or distances are combined in a linear way without using speed ratios. - 29 m: This is the simple sum of 25 m and 4 m, but adding leads like this is not valid.

Common Pitfalls:
The main error is to believe that if A beats B by 25 m and B beats C by 4 m, then A beats C by 25 + 4 = 29 m. This ignores that all runners take different times to reach those distances. Always derive the ratio of speeds, then reapply that ratio to the race distance of interest. That is the only reliable approach for such questions.

Final Answer:
In the 100 m race, A beats C by 28 m.