In a 1 km race, A beats B by 50 m. In a 500 m race, B beats C by 50 m. By how many metres will A beat C in an 800 m race?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 116 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 950 m: A : B \(=1000:950\)
When B runs 500 m, C runs 450 m: B : C \(=500:450=10:9\)
When A runs 1000 m, B runs 950 m and C runs \(\displaystyle 950\times\frac{9}{10}=855\) m
When A runs 800 m, C runs \(\displaystyle 800\times\frac{855}{1000}=684\) m
A beats C by \(800-684=116\) m
A beats C by 116 m.