Question

In a game, A can give 20 points to B, A can give 32 points to C and B can give 15 points to C. How many points make the game?

• A. 80
• B. 70
• C. 100
• D. 60

Hint:

"A gives x points to B" means A plays 100% capacity and B plays at (100-x)% capacity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Let \( G \) be the points in the game. When A gives \( x \) points to B, it means A reaches \( G \) when B is at \( G-x \).
The ratio of their speeds (or performances) is \( A/B = G/(G-x) \).

Step 2: Key Formula or Approach:
1) A gives 20 to B: \( A/B = G/(G-20) \)
2) A gives 32 to C: \( A/C = G/(G-32) \)
3) B gives 15 to C: \( B/C = G/(G-15) \)

Step 3: Detailed Explanation:
Since \( A/C = (A/B) \times (B/C) \):
\[ \frac{G}{G-32} = \frac{G}{G-20} \times \frac{G}{G-15} \]
Divide by \( G \):
\[ \frac{1}{G-32} = \frac{G}{(G-20)(G-15)} \]
\[ G^2 - 35G + 300 = G^2 - 32G \]
\[ 3G = 300 \implies G = 100 \]

Step 4: Final Answer:
The game is of 100 points.