Discussion

At a game billiards, A can give B 10 points in 60 and he can give C 15 in 60. How many can B can give C in a game of 90?

Answer: A

In these problems the two runners are compared by the distances they cover in the same time, so their speeds are in the ratio of those distances.

\[ \text{A } 60 : \text{B } 50, \qquad \text{A } 60 : \text{C } 45 \]

Both are stated against the same A score of 60, so B and C compare directly:

\[ B : C = 50 : 45 \]

In a game of 90, when B scores 90:

\[ C = 90 \times \frac{45}{50} = 81 \]

\[ \text{B can give C} = 90 - 81 = 9 \text{ points} \]

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