Translating comparative strength across games: In a game, A can give B 25 points in 75 and C 18 points in 90. In a 120-point game, how many points can C give B?

Introduction / Context:We convert handicaps into scoring speed ratios, compare B and C, then project to the requested game length.

Given Data / Assumptions:

• A vs B (75): A:B = 75:50 = 3:2.
• A vs C (90): A:C = 90:72 = 5:4.
• Uniform scoring rates.

Concept / Approach:From A:B = 3:2 and A:C = 5:4 ⇒ B:C = (2/3)/(4/5) = (2/3)*(5/4) = 10/12 = 5/6. C is faster than B (denominator smaller time for same points).

Step-by-Step Solution:

Verification / Alternative check:Both frames (B finishing at 120 or C finishing at 120) are consistent with a 20-point handicap.

Why Other Options Are Wrong:30/40/50 arise from mis-scaling or difference-based thinking rather than ratio-based.

Common Pitfalls:Using absolute point gaps instead of relative scoring speeds when changing game length.

Final Answer:20