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

120 points
90 points
80 points
100 points
Explanation:

Let x points make the game

A can give B 20 points, A can give C 32 points

=> When A scores x points, B scores $\left(x-20\right)$ points and C scores $\left(x-32\right)$ points

B can give C 15 points

=> When B scores x points, C scores $\left(x-15\right)$ points

$\text{=> When B scores 1 point, C scores }\dfrac{(x-15)}{x}\text{ points}$

$\text{=> When B scores $\left(x-20\right)$ point, C scores }\dfrac{(x-20)(x-15)}{x}\text{ points}$

$\text{i.e., } \left(x-32\right) = \dfrac{(x-20)(x-15)}{x}$

$\Rightarrow x(x-32) = (x-20)(x-15)$

$\Rightarrow x^2 - 32x = x^2 - 35x + 300$

$\Rightarrow - 32x = - 35x + 300$

$\Rightarrow 3x = 300$

$\Rightarrow x = 100$

i.e., 100 points make the game

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