In a 300 m race, A beats B by 30 m and C by 40 m. In a race of 540 m, B will beat C by -

Question: In a 300 m race, A beats B by 30 m and C by 40 m. In a race of 540 m, B will beat C by -

Solution:
Given that,
A : B = 300 : 270
and A : C = 300 : 260

A/B = 300/270
and A/C = 300/260

∴ B/C = (B/A) × (A/C)
⇒(270/300) × (300/260) = 270/260
⇒ (270 × 2)/(260 × 2) = 540/520
⇒ B/C = 540/520

∴ B : C = 540 : 520

∴ In a 360 m race, B beats C by (540 - 520) m = 20 m