In a 900m race, A can beat B by 100 m. In a 700 m race, B can beat C by 70 m. By how many meters will A beat C in a race of 600 m?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120 m
In a 900 m race, when A has run 900 m, B has run 800 m. So the speeds of A and B are in the ratio 9 : 8.
In a 700 m race, when B has run 700 m, C has run 630 m. So the speeds of B and C are in the ratio 10 : 9.
Combining the two ratios,
\( \displaystyle \frac{A}{C}=\frac{9}{8}\times\frac{10}{9} \)
\( \displaystyle =\frac{5}{4} \)
In a 600 m race, when A finishes, C has run
\( \displaystyle 600\times\frac{4}{5}=480\ \text{m} \)
So A beats C by \( 600-480=120 \) m.
CBSE Applied Mathematics (Class XII):
Races and Games
