In a 90-point game, A can give B 15 points and C 30 points. How many points can B give C in a 100-point game?

Introduction / Context:
Again we convert handicaps to relative strengths and then translate to a new target total. “A gives B 15 in 90” ⇒ when A scores 90, B scores 75. “A gives C 30 in 90” ⇒ when A scores 90, C scores 60.

Given Data / Assumptions:

• A:B:C = 90:75:60 = 6:5:4.

Concept / Approach:
Thus B:C = 5:4. In a game to 100 for B, C’s equivalent score would be 100*(4/5) = 80, so B can give C 20 points.

Step-by-Step Solution:

Verification / Alternative check:
Proportional scores (5:4) hold consistently.

Why Other Options Are Wrong:
30 or 50 violate the 5:4 proportionality; 140 is nonsensical for a 100-point target.

Common Pitfalls:
Mixing the 90-point base with the 100-point question without re-scaling.

Final Answer:
20