In a race of 500m, A can beat B by 50m. In a race of 450m, B beats C by 50m. By how many metres will A beat C in a race of 1500 m?

In a race of 500m, A beats B by 50m

⇒ A : B = 500 : 450

In a race of 450m, B beats C by 50m

⇒ B : C = 450 : 400

Now,

$(\frac{A}{C} = \;\frac{A}{B} \times \frac{B}{C})$

$( \Rightarrow \frac{A}{C} = \;\frac{{500}}{{450}} \times \frac{{450}}{{400}})$

$( \Rightarrow \frac{A}{C} = \;\frac{5}{4})$

⇒ When A covers 5m, C covers 4m.

⇒ When A covers 1500m, C will cover $(\frac{4}{5} \times 1500 = 1200m)$

∴ In a race of 1500m, A beats C by (1500 - 1200) = 300m.