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?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100
Let the game be of G points. When A scores G, B scores G − 20 and C scores G − 32. When B scores G, C scores G − 15. The ratio of the scores of C and B is the same in both cases:
\( \displaystyle \frac{G-32}{G-20}=\frac{G-15}{G} \)
\( \displaystyle G^2-32G=G^2-35G+300 \)
\( \displaystyle 3G=300 \)
\( \displaystyle G=100 \)