A can run 45 m while B runs 50 m. In a 1000 m race, by how many metres does B beat A?

Introduction / Context:Comparative speed statements like “A runs 45 m while B runs 50 m” define a speed ratio. Converting that ratio into a race margin requires scaling distances to the race length for the faster runner and reading off how far the slower runner gets in the same time.

Given Data / Assumptions:

• Speed ratio A:B = 45:50 = 9:10.
• B completes 1000 m; find A's distance at that instant.

Concept / Approach:For equal time, distances are proportional to speeds. When B runs 10 “parts,” A runs 9 “parts.” Scale to 1000 m for B and compute A's distance.

Step-by-Step Solution: When B = 1000 m (10 parts), A = (9/10) * 1000 = 900 m Lead of B over A = 1000 − 900 = 100 m

Verification / Alternative check:Equivalently, speed ratio 10:9 implies B is 11.11% faster; over 1000 m, that translates to a 100 m margin.

Why Other Options Are Wrong:150, 200, 125 m do not correspond to the exact 9:10 proportional distance in the same time frame.

Common Pitfalls:Using time ratios instead of distance for equal-time comparison; mixing up which athlete is faster (here B is faster).

Final Answer:100 m