In a 1000 m race, A beats B by 100 m and C by 200 m. By how much does B beat C in a 1350 m race?

Introduction / Context:
When margins versus a common competitor are known, convert them to speed ratios, then compare the two remaining competitors over a new distance by scaling with those ratios.

Given Data / Assumptions:

• When A runs 1000 m, B runs 900 m, and C runs 800 m.
• Speeds are proportional to these distances over equal time: A:B:C = 1000:900:800 = 10:9:8.
• We compare B and C over 1350 m.

Concept / Approach:
For equal times, distance ∝ speed. When B finishes 1350 m, C covers (speed_C/speed_B) times that distance.

Step-by-Step Solution:
speed_B : speed_C = 9 : 8 C's distance when B finishes = 1350 * (8/9) = 1200 m Lead of B over C = 1350 − 1200 = 150 m

Verification / Alternative check:
Consistent with the 10:9:8 baseline; margins scale linearly with course length for uniform speeds.

Why Other Options Are Wrong:
125, 130, 140 m are not the exact scaled difference implied by the 9:8 speed ratio over 1350 m.

Common Pitfalls:
Using 100 m vs 200 m differences directly without forming ratios; forgetting to scale the margin for the new race length.

Final Answer:
150 m