In a 10 km race, A, B and C each run at uniform speed, get the first, second and third position respectively. If A beats B by 1 km and B beats C by 1 km, then, by how much distance A beat C?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.9 km
Since the speeds are uniform, the distances covered in the same time are in the ratio of the speeds.
When A runs 10 km, B runs 9 km. When B runs 10 km, C runs 9 km, so in any time
\( \displaystyle \frac{\text{distance of C}}{\text{distance of B}} = \frac{9}{10} \)
When A finishes, B has run 9 km, so C has run
\( \displaystyle 9 \times \frac{9}{10} = 8.1 \text{ km} \)
A beats C by \(10 - 8.1 = 1.9\) km
Tip: The two leads cannot simply be added (1 + 1 = 2 km). B beats C by 1 km over B’s full 10 km, but when A finishes, B has run only 9 km.
CBSE Applied Mathematics (Class XII):
Races and Games
