Question

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

• A. 30 points
• B. 10 points
• C. 20 points
• D. 12 points

Answer 1

Answer:

B. 10 points

1. Points of A and B: When A finishes (60 points) in a 60 point game, A gives up 15 points to B. That means B gets: $60 - 15 =$45 points.

2. Points of A and C: When A finishes the same 60 point game, A gives up 20 points to C. That means C gets: $60 - 20 =$40 points.

3. Ratio between the points of B and C: Now we know that B scores 45 points while C scores only 40 points.

The ratio of their abilities is as follows:

$\frac{C}{B} = \frac{40}{45} = \frac{8}{9}$

In a game of 90 points: We need to find how many points C will score when B scores 90 points. For this, when B's score is 90:

$C = 90 \times \frac{8}{9} = 80 \text{ points.}$

While B can score 90 points, C can only score 80 points. Therefore, the points that B can give to C are: $90 - 80 = \mathbf{10}$ points.