In a 1 km race, A beats B by 100 m. In a 400 m race, B beats C by 40 m. By how many metres will A beat C in a 500 m race?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 95 m
Running at steady speeds, the distances covered in the same time are in the ratio of the speeds. Linking A with B and B with C gives A with C.
When A runs 1000 m, B runs 900 m: A : B \(=1000:900\)
When B runs 400 m, C runs 360 m: B : C \(=400:360=10:9\)
When A runs 1000 m, B runs 900 m and C runs \(\displaystyle 900\times\frac{9}{10}=810\) m
When A runs 500 m, C runs \(\displaystyle 500\times\frac{810}{1000}=405\) m
A beats C by \(500-405=95\) m
A beats C by 95 m.