In a race of 800 m, A beats B by 80 m and in a race of 600 m, B beats C by 40 m. Then A will beat C in a race of 1000 m by :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 160 m
When A runs 800 m, B runs 800 − 80 = 720 m; when B runs 600 m, C runs 600 − 40 = 560 m. The speeds are in the ratio of the distances covered in the same time:
\( \displaystyle A:B=800:720=10:9 \)
\( \displaystyle B:C=600:560=15:14 \)
Make the B terms equal (LCM of 9 and 15 is 45):
\( \displaystyle A:B=50:45 \)
\( \displaystyle B:C=45:42 \)
\( \displaystyle A:C=50:42=25:21 \)
So when A runs 1000 m, C runs
\( \displaystyle 1000\times\frac{21}{25}=840\ \text{m} \)
A beats C by 1000 − 840 = 160 m.
Why the other options are incorrect
Option (1) 120 m — Incorrect. 120 m is the sum of the two leads, 80 + 40; leads from races of different lengths cannot simply be added.
Option (2) 150 m — Incorrect. The lead is 160 m, not 150 m.
Option (4) 172 m — Incorrect. The lead is 160 m, not 172 m.
CBSE Applied Mathematics (Class XII):
Races and Games
