In a 100 m race, A beats B by 25 m and B beats C by 4 m. In the same race, by how many metres does A beat C?

Problem restatementFrom two head-start results, deduce A vs. C gap over 100 m.

Given data

• A : B speeds = 100 : 75 = 4 : 3.
• B : C speeds = 100 : 96 = 25 : 24.

Concept/ApproachMultiply ratios to get A : C speed ratio, then compute C's distance when A finishes 100 m.

Step-by-step calculation A : C = (A : B) × (B : C) = (4/3) × (25/24) = 100/72 = 25/18 C's distance when A finishes = 100 × (18/25) = 72 m Margin (A over C) = 100 − 72 = 28 m

Verification/AlternativeChain-speed method ensures consistency across racers; the 28 m result matches standard composition of ratios.

Final Answer28 m