In a game of billiards, A can give B, 15 points in 60 and A can give C, 20 points in 60. How many points can B give C in a game of 90?

When A finishes scoring 60 points, B has only scored 45 points (60 - 15 = 45).

When A finishes scoring 60 points, C has only scored 40 points (60 - 20 = 40).

The question asks: when B scores 90 points in a game, how many points can B give C?

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Finding the ratio of A to B:

A scores: 60

B scores: 45

Ratio A:B = 60:45 = 4:3

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Finding the ratio of A to C:

A scores: 60

C scores: 40

Ratio A:C = 60:40 = 3:2

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To compare B and C directly, make A the same value in both ratios.

A:B = 4:3

Multiplying by 3: A:B = 12:9

A:C = 3:2

Multiplying by 4: A:C = 12:8

Since A = 12 in both ratios:

B:C = 9:8

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When B scores 9 points, C scores 8 points.

Scaling up to a game where B scores 90:

$\dfrac{B}{C} = \dfrac{9}{8} = \dfrac{90}{80}$

When B scores 90, C scores 80.

Points B can give C = 90 - 80 = 10

Therefore, B can give C 10 points in a game of 90.