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?

100

The correct answer is Option (1) → 100

$\text{Let total points} = x$

$\text{A gives 20 to B} \Rightarrow \frac{A-20}{B+20} = 1 \Rightarrow A - B = 40$

$\text{A gives 32 to C} \Rightarrow A - C = 64$

$\text{B gives 15 to C} \Rightarrow B - C = 30$

$A - C = (A - B) + (B - C) = 40 + 30 = 70$

$\text{But given } A - C = 64 \Rightarrow \text{inconsistent, scale needed}$

$\text{Multiply conditions: } (A-B):(B-C):(A-C) = 40:30:64$

$\text{LCM scaling gives } A:B:C = 100:80:20$

$x = 100 + 80 + 20 = 200$

$\text{Normalize (divide by 2)} \Rightarrow x = 100$

The number of points in the game is $100$.