In a kilometer race, A beats B by 100 meters and B beats C by 125 meters. Then A beats C by
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 212.5 meters
A kilometre is 1000 m. While A runs 1000 m, B runs 900 m; while B runs 1000 m, C runs 875 m.
C's distance is in the same ratio to B's in any time, so while B runs 900 m,
\( \displaystyle \text{C runs}\ 900\times\frac{875}{1000}=787.5\ \text{m} \)
So when A finishes 1000 m, C has run 787.5 m:
\( \displaystyle \text{A beats C by }1000-787.5=212.5\ \text{m} \)
Why the other options are incorrect
Option (1) 25 meters — Incorrect. 25 m is 125 − 100, which subtracts the two margins; margins in a race do not combine by subtraction.
Option (2) 200 meters — Incorrect. A beats C by 212.5 m, not 200 m.
Option (4) 225 meters — Incorrect. 225 m simply adds 100 and 125, but B's 125 m lead is over 1000 m of B's running, and B runs only 900 m while A finishes.
CBSE Applied Mathematics (Class XII):
Races and Games
