In a 200 m race A beats by B by 20m,
$∴ A:B = 200 : (200-20) = 200:180$
$∴ B:C = 250 : (250-10) = 250:240$
$∴ \dfrac{A}{B} \times \dfrac{B}{C} = \dfrac{200}{180} \times \dfrac{250}{240} = \dfrac{A}{C} = \dfrac{125}{108}$
∴ When A covers 125m , C covers 108 m
Or, when A covers 1000m (1km) C covers $\dfrac{108}{125}\times 1000 = 864 m$
$\color{green}{\text{∴ A beats C by (1000 - 864)m =}}$ $\color{red}{136m}$ $\color{green}{\text{in a 1000m or 1km race}}$