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?
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A10
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B90
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C15
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D85
Answer
Correct Answer: 10
Explanation
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:
When B scores 100, C would score 100*(9/10) = 90.Thus, B can give C = 100 − 90 = 10 points.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