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

10 points

The correct answer is Option (1) → 10 points

In a 100–point game, when A gives $20$ points to B, then

Ratio of strengths $A:B = 100:80 = 5:4$.

When A gives $28$ points to C, then

Ratio of strengths $A:C = 100:72 = 25:18$.

Thus

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

So

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

If B gives $x$ points to C in a 100–point game, then

$\frac{100}{100-x}=\frac{10}{9}$

$100-x=90$

$x=10$

final answer: $10$ points