In billiards, A can give B 15 points in a game to 60, and A can give C 20 points in a game to 60. In a game to 90, how many points can B give C?

Problem restatementHandicaps: when A reaches 60, B has 45 and C has 40. Determine B's handicap over C in a game to 90.

Given data

• Relative scoring in same time: A:B:C = 60:45:40 = 12:9:8.

Concept/ApproachUse proportional scoring rates: in the time B scores 90, C scores (rate ratio) × 90.

Step-by-step calculation v_B : v_C = 9 : 8 C's score when B reaches 90 = (8/9) × 90 = 80 Therefore, B can give C = 90 − 80 = 10 points

Verification/AlternativeConsistency with 60-point data: scaling 45 and 40 by 2 gives 90 and 80 respectively.

Final Answer10 points