In a game of 100 points, 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 reflect scoring rate ratios. If A gives B and C certain points to 100, we can compute A:B and A:C rate ratios and then deduce B:C and the corresponding head start in a 100-point game.

Given Data / Assumptions:

• When A scores 100, B scores 80 ⇒ A:B = 100:80 = 5:4.
• When A scores 100, C scores 72 ⇒ A:C = 100:72 = 25:18.

Concept / Approach:
Rates are proportional to scores in equal time. Use B/A = 4/5 and C/A = 18/25 to find B/C = (B/A)/(C/A). Translate the ratio into a points head start out of 100.

Step-by-Step Solution:
B/A = 4/5, C/A = 18/25 B/C = (4/5) / (18/25) = (4/5) * (25/18) = 100/90 = 10/9 If B scores 100, C scores 90 ⇒ B can give C 10 points in 100.

Verification / Alternative check:
Check consistency: A:B:C speeds ∝ 5:4 and 25:18 ⇒ B:C = 10:9 as derived.

Why Other Options Are Wrong:
12, 15, 20 points imply different B:C ratios not supported by the given head starts versus A.

Common Pitfalls:
Adding/subtracting head starts directly instead of forming rate ratios; mis-scaling to a 100-point target.

Final Answer:
10 points