Discussion

In a game of Snooker, A can Give B 16 Points in 80 and A can Give C 15 point in 90. How many points can C give B in a game of 50?

Answer: D

In these problems the two players are compared by the scores they reach in the same time, so their rates are in the ratio of those scores.

The two handicaps are quoted over different totals, so scale both to a common basis.

\[ A\,80 : B\,64 \ \Rightarrow\ B = \tfrac{4}{5}A \]

\[ A\,90 : C\,75 \ \Rightarrow\ C = \tfrac{5}{6}A \]

\[ \frac{C}{B} = \frac{5/6}{4/5} = \frac{25}{24} \]

C is the stronger, so in a game of 50, when C reaches 50:

\[ B = 50 \times \frac{24}{25} = 48 \]

\[ \text{C can give B} = 50 - 48 = 2 \text{ points} \]

The two handicaps cannot be compared directly, since one is over 80 and the other over 90.

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