Runner A can run 22.5 m in the same time that runner B runs 25 m. In a 1 km race, by how many metres will B beat A?

Introduction / Context:
This question directly compares the speeds of two runners A and B by giving the distances each covers in the same time. From this we can form a speed ratio and then predict the outcome of a longer race. Such questions are simple but powerful tests of ratio handling and basic proportional reasoning in aptitude exams.

Given Data / Assumptions:
- In some equal time interval, A runs 22.5 m while B runs 25 m. - Race length is 1 kilometre, that is 1000 m. - Both runners maintain constant speeds during the race. - We must find B's lead over A at the finish line.

Concept / Approach:
If distances covered in the same time are 22.5 m and 25 m, then the ratio of speeds vA : vB is 22.5 : 25. From that, we can find how far A runs in the time B takes to run 1000 m. The difference in distances at that time gives B's winning margin in metres.

Step-by-Step Solution:
Step 1: vA : vB = 22.5 : 25. Step 2: Divide numerator and denominator by 2.5 to simplify: 22.5 / 2.5 = 9 and 25 / 2.5 = 10. So vA : vB = 9 : 10. Step 3: Express vA = 9k and vB = 10k for some constant k. Step 4: Time for B to run 1000 m is TB = 1000 / (10k). Step 5: In time TB, A covers distance = vA * TB = 9k * 1000 / (10k) = 900 m. Step 6: Therefore, when B finishes 1000 m, A is at 900 m, so B beats A by 1000 - 900 = 100 m.

Verification / Alternative check:
We can normalise time so that the common interval is 1 unit. Then A's speed is 22.5 m per unit time and B's speed is 25 m per unit time. To find A's distance when B has run 1000 m, scale by the ratio 22.5 / 25 = 0.9. Then A's distance is 0.9 * 1000 = 900 m, leaving a gap of 100 m, which agrees with the previous calculation and confirms the result.

Why Other Options Are Wrong:
- 111 m and 50 m: These margins do not correspond to the 9 : 10 speed ratio and would imply different relative speeds. - 25 m: Much too small, and it would only match a ratio closer to 25 : 26 instead of 9 : 10.

Common Pitfalls:
An error seen often is to subtract 22.5 from 25 and treat the 2.5 m difference as a constant gap over the whole race, then scale it incorrectly. Another issue is forgetting to convert the 1 km race into 1000 m. The safe approach is always to use ratios of speeds and then apply them to the exact race distance mentioned.

Final Answer:
In the 1 km race, B will beat A by 100 m.