Discussion

In a 2 Km race, P can give Q 200 m and R 560 m. In the same race, Q can give R

Answer: A

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.

\[ P\,2000 : Q\,1800, \qquad P\,2000 : R\,1440 \]

\[ Q : R = 1800 : 1440 = 5 : 4 \]

In a 2000 m race, when Q finishes:

\[ R = 2000 \times \frac{4}{5} = 1600 \text{ m} \]

\[ \text{Q can give R} = 2000 - 1600 = 400 \text{ m} \]

The difference of the starts, \( 560 - 200 = 360 \), is not the answer - Q's advantage is measured over a shorter effective run.

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