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1. A runs 123 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

Solution:
Ratio of speeds of A and B =53:1=5:3
Thus, in race of 5m, A gains 2m over B
2m are gained by A in a race of 5m
80m will be gained by A in a race of
(52×80)m=200 m
∴ Winning post is 200 m away from the starting point

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