In a 1-kilometre race, A can beat B by 30 meters, while in a 500-meter race B can beat C by 25 meters. By how many meters will A beats C in a 100-meter race?

Answer: Option A

When A runs 100 meters, B runs 970 meters.
Hence, when A runs 100 meter, b runs 97 meter.
When B runs 500 meter, C runs 475 meter.
When B runs 97 meter, C runs, $$\frac{475\times 97}{500}$$   = 92.15 meter.
Hence,
A will beat C by (100 - 92.15) = 7.85 meters.