In a 100 m race, A beats B by 10 m and C by 13 m. In a 180 m race, by how many metres will B beat C?

Problem restatement
Use two margins against A to infer B vs. C speed ratio, then scale to 180 m.

Given data

• v_A : v_B = 100 : 90 = 10 : 9.
• v_A : v_C = 100 : 87.

Concept/Approach
Compute v_B : v_C = (v_B/v_A) × (v_A/v_C) and then the distance C covers when B runs 180 m.

Step-by-step calculation
v_B/v_C = (90/100) × (100/87) = 90/87 = 30/29 C's distance when B runs 180 m = (29/30) × 180 = 174 m Margin (B over C) = 180 − 174 = 6 m

Verification/Alternative
Direct scaling from 100 m margins leads to same ratio; 6 m is the consistent result.

Final Answer
6 m