In a game played to 100 points, player A can give B a start of 20 points and can give C a start of 28 points. How many points can B give C?

Introduction / Context:
This problem repeats the same game setup as an earlier question but asks again for the handicap B can give C. It reinforces the idea that scoring abilities can be compared through ratios derived from how many points each player scores when another reaches a fixed target score.

Given Data / Assumptions:
- Target score in the game is 100 points. - When A scores 100, B scores 80 points. - When A scores 100, C scores 72 points. - Scoring rates are constant and proportional to these scores. - We must find how many points B can give C in a game to 100 points.

Concept / Approach:
We interpret these statements as ratios of scoring rates. A to B has ratio 100 : 80, and A to C has 100 : 72. Using these, we find the ratio B : C and then deduce how many points C will score while B scores 100. The difference between 100 and that score is the handicap B can give C.

Step-by-Step Solution:
Step 1: From A and B, vA : vB = 100 : 80 = 5 : 4. Step 2: From A and C, vA : vC = 100 : 72 = 25 : 18. Step 3: Express vB = (4/5) * vA and vC = (18/25) * vA. Step 4: Ratio vB : vC = (4/5) : (18/25) = (4/5) * (25/18) = 100 / 90 = 10 / 9. Step 5: If B scores 100 points, C scores (9/10) * 100 = 90 points in the same time. Step 6: Therefore B can give C a start of 10 points in a 100 point game.

Verification / Alternative check:
Take vA = 50 units. Then vB = 40 units and vC = 36 units. Time for B to reach 100 points is 100 / 40 = 2.5 units. In that time C scores 36 * 2.5 = 90 points. So if B starts from 0 and C starts from 10, both reach 100 together, which confirms that 10 points is the correct handicap.

Why Other Options Are Wrong:
- 8 points and 14 points: These do not match the exact 10 : 9 ratio and lead to mismatched finishing scores. - 40 points: This implies C is extremely weak, which contradicts the given ratios that show C is only slightly weaker than B.

Common Pitfalls:
Many learners skip the ratio step and manipulate raw point differences directly. Another mistake is reversing who gives whom points. Always start from the meaning of a handicap, convert it into a rate ratio, and then compute the handicap between the other pair using these derived ratios.

Final Answer:
B can give C a start of 10 points in a 100 point game.