In a 100-point game, A can give B 20 points and C 28 points. How many points can B give C in a 100-point game?

Introduction / Context:
Point handicaps translate to proportional scoring strengths. “A gives B 20 in 100” means when A scores 100, B scores 80. We can find relative strengths and then deduce a fair handicap between B and C for the same target score.

Given Data / Assumptions:

• A:B = 100:80 = 5:4.
• A:C = 100:72 = 25:18 (or 5:3.6).

Concept / Approach:
Normalize with A as common reference. From A:B = 5:4 and A:C = 25:18 ⇒ set A = 25 units ⇒ B = 20 units; C = 18 units. Then B:C = 20:18 = 10:9.

Step-by-Step Solution:

Verification / Alternative check:
Scaling by any common factor preserves the 10:9 ratio.

Why Other Options Are Wrong:
15 or 85/90 misrepresent the proportional difference.

Common Pitfalls:
Adding/subtracting 20 and 28 directly rather than converting to ratios first.

Final Answer:
10