In a 100 m race, runner A covers the distance in 36 seconds and runner B covers it in 45 seconds. In this race, by how many metres does A beat B?

Introduction / Context:
This is a straightforward race question where we know the times taken by two runners to cover the same distance. We must find by how much distance the faster runner leads when he finishes the race. Such questions reinforce the idea that when distance is fixed, faster speed means less time, and we can work back to distance covered by the slower runner in the same time.

Given Data / Assumptions:
- Race distance is 100 m. - A takes 36 seconds to run 100 m. - B takes 45 seconds to run 100 m. - Each runner runs at constant speed. - We must find A's lead over B at the moment A finishes.

Concept / Approach:
We find the speed of B by using distance over time, then compute how far B runs in the 36 seconds that A needs to complete his 100 m. The difference between 100 m and this distance is A's winning margin. There is no need to compute A's speed directly, though we could do so as a check.

Step-by-Step Solution:
Step 1: Speed of B = distance / time = 100 / 45 m per second. Step 2: Time taken by A to finish the race is 36 seconds. Step 3: In 36 seconds, distance covered by B = (100 / 45) * 36. Step 4: Simplify: 36 / 45 = 4 / 5, so distance by B = 100 * 4 / 5 = 80 m. Step 5: Lead of A over B = 100 - 80 = 20 m.

Verification / Alternative check:
Compute A's speed also for confirmation. A's speed is 100 / 36 m per second. Time taken to cover 80 m at B's speed 100 / 45 is 80 * 45 / 100 = 36 seconds. That means that when A finishes in 36 seconds, B has indeed run 80 m, so the 20 m lead is consistent from both perspectives.

Why Other Options Are Wrong:
- 25 m and 22.5 m: These correspond to incorrect manipulation of the ratio 36 : 45, and do not match the exact 4 : 5 simplification. - 9 m: This is far too small and could arise from confusing time difference with distance difference.

Common Pitfalls:
Some learners directly subtract the times 45 and 36 and then try to convert that into a distance for A, not B, which creates confusion. Another mistake is to assume that the difference in times translates linearly into difference in distances at the same speed. Always compute the slower runner's distance in the faster runner's finishing time by using the slower runner's speed explicitly.

Final Answer:
In the 100 m race, A beats B by 20 m.