In a kilometer race, A can beat B by 100 m. In a race of 400 m, B can…

The correct answer is Option (2) → 95m

“A beats B by 100 m in 1000 m” means that while A runs 1000 m, B runs 900 m. The ratios of distances covered in the same time are

    \( \displaystyle \frac{B}{A}=\frac{900}{1000}=\frac{9}{10} \)

    \( \displaystyle \frac{C}{B}=\frac{400-40}{400}=\frac{9}{10} \)

Multiplying the ratios:

    \( \displaystyle \frac{C}{A}=\frac{9}{10}\times\frac{9}{10}=\frac{81}{100} \)

While A runs 500 m, C runs

    \( \displaystyle 500\times\frac{81}{100}=405\text{ m} \)

So A beats C by 500 − 405 = 95 m.