In a race of 1200 meters, A can beat B by 120 meters and in a race of 800 meters B can beat C by 40 meters. In a race of 400 meters, by how many meters can A beat C?

Given:

When A runs 1200 m, B runs 1200 − 120 = 1080 m

When B runs 800 m, C runs 800 − 40 = 760 m

Formula used:

Speed ∝ Distance (for same time)

If A beats B by x meters in d meters race ⇒ Speed of A : B = d : (d − x)

Calculation:

Speed of A : B = 1200 : 1080 = \(\dfrac{1200}{1080} = \dfrac{10}{9}\)

Speed of B : C = 800 : 760 = \(\dfrac{800}{760} = \dfrac{20}{19}\)

⇒ Speed of A : C = A : B × B : C = \(\dfrac{10}{9} \times \dfrac{20}{19} = \dfrac{200}{171}\)

Now in 400 m race, A runs full 400 m, so C runs:

\(\dfrac{171}{200} \times 400 = 342\) meters

⇒ A beats C by = 400 − 342 = 58 meters

∴ The correct answer is 58 meters.