In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C?

10 points

The correct answer is Option (4) → 10 points **

$\text{A gives B 20 points in 100} \;\Rightarrow\; A:B = 100:80 = 5:4$

$\text{A gives C 28 points in 100} \;\Rightarrow\; A:C = 100:72 = 25:18$

From $A:B = 5:4$ and $A:C = 25:18$:

$\frac{B}{C}=\frac{4}{5}\times\frac{25}{18}=\frac{100}{90}=\frac{10}{9}$

$\text{If B gives C }x\text{ points in 100: } \frac{100}{100-x}=\frac{10}{9}$

$900 = 1000 - 10x$

$10x = 100$

$x = 10$

B can give C 10 points.