[200 m] A runs 1 \dfrac{2}{3} times as fast as B. If A gives B a start of 80 m, how far must the winning

For Competitive Exams

A runs 1$ \dfrac{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?

200 m

300 m

270 m

160 m

Explanation:

Ratio of the speeds of A and B =$ \dfrac{5}{3} $: 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$ \left(\dfrac{5}{2} \times 80\right) $m= 200 m.

$\therefore$ Winning post is 200 m away from the starting point.

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