Races A beats B and B beats C

• When A covers 100 m, B covers $100 - 10 = 90$ m. So $V_A : V_B = 100 : 90 = 10 : 9$.
• When B covers 100 m, C covers $100 - 5 = 95$ m. So $V_B : V_C = 100 : 95 = 20 : 19$.

Combining the ratios: $\frac{V_A}{V_C} = \frac{10}{9} \times \frac{20}{19} = \frac{200}{171}$

When A covers 100 m, distance covered by C = $100 \times \frac{171}{200} = 85.5$ m.

Thus, A beats C by $100 - 85.5 = 14.5$ meters.