A runs $$1\frac{2}{3}$$ 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?

A. 200 m

B. 300 m

C. 270 m

D. 160 m

Answer: Option A

Solution(By Examveda Team)

Ratio of speeds of A and B $$ = \frac{5}{3}:1 = 5:3$$
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
$$\left( {\frac{5}{2} \times 80} \right){\text{m}} = 200{\text{ m}}$$
∴ Winning post is 200 m away from the starting point