Question

In a race of 800 metres, A can beat B by 40 metres.
In a race of 500 metres, B can beat C by 5 metres.
In a race of 200 metres, A can beat C by

• A. $11.9$ metres
• B. $1.19$ metres
• C. $12.74$ metres
• D. $1.27$ metres

Answer 1

The correct option is A $11.9$ metres

When $A$ runs $800$ meters, $B$ runs $760$ meters and when $B$ runs $500$ meters, $C$ runs $495$ meters.

$\therefore$, when $B$ runs $760$ meters, the distance that $C$ runs $=\frac{(760\times 495)}{500}=\frac{376,200‬}{500}=752.4$ meters.

So, in a race of $800$ meters, $A$ beats $C$ by $(800-752.5)=47.5‬$ meters to $C$.

So, in a race of $200$ meters, the number of meters by Which $A$ beats $C=\frac{(200\times 47.5)}{800}=11.875‬\approx 11.9$ meters.