In a game, A can give 36 points to B, A can give 42 points to C, B ca…

The correct answer is Option (3) → 90 points

Let the game be of N points. “A can give 36 points to B” means that when A scores N, B scores N − 36. So, while A scores N, B scores N − 36 and C scores N − 42, which gives

    \( \displaystyle \frac{B}{C} = \frac{N - 36}{N - 42} \)

“B can give 10 points to C” means that when B scores N, C scores N − 10:

    \( \displaystyle \frac{B}{C} = \frac{N}{N - 10} \)

Equating the two ratios of scores:

    \( \displaystyle \frac{N - 36}{N - 42} = \frac{N}{N - 10} \)

    \((N - 36)(N - 10) = N(N - 42)\)

    \(N^2 - 46N + 360 = N^2 - 42N\)

    \(4N = 360\)

    \(N = 90\)

Check: in a game of 90, B scores 54 and C scores 48 while A scores 90; then \(54 : 48 = 90 : 80\), so B gives C 10 points.