Question

In a race of $1000$ meters, $A$ can beat $B$ by $100$ meters, in a race of $800$ meters, $B$ can beat $C$ by $100$ meters. By how many meters will $A$ beat $C$ in a race of $600$ meters?

Answer 1

When $A$ runs $1000$ meters, $B$ runs $900$ meters and when $B$ runs $800$ meters, $C$ runs $700$ meters.

$\therefore$, when $B$ runs $900$ meters, the distance that $C$ runs $=\frac{(900\times 700)}{800}=\frac{6300}{8}=787.5$ meters.

So, in a race of $1000$ meters, $A$ beats $C$ by $(1000-787.5)=212.5$ meters to $C$.

So, in a race of $600$ meters, the number of meters by Which $A$ beats $C=\frac{(600\times 212.5)}{1000}=127.5$ meters.