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?

Ratio of the speeds of A and B =5 : 1 = 5 :3

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

80 m will be gained by A in race of $\frac{5}{2}*80$ m =200m

=> Winning post is 200 m away from the starting point.