A beats B by 100 m and C by 150 m in a kilometer race. In the same race, by how many meters does B beat C in that race?

Question: A beats B by 100 m and C by 150 m in a kilometer race. In the same race, by how many meters does B beat C in that race?

Solution:
Here,
A : B = 1000 : 900
A : C = 1000 : 850

B/C = B/A / C/A
= (B/A) × (A/C)
= (900/1000) × (1000/850)
= 900/850

in 900m B beats C by 50m
∴ in 1000m B beats C by = (50 × 1000)/900 = 50000/900 = 55.55m