Question:
Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?
Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?
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From the first race find the ratio of the two speeds, then see how far each has run when the faster runner completes his distance in the second race.
Updated On: Nov 4, 2026
- Karan beats Arjun by 1 metre.
- Arjun beats Karan by 1 metre
- Arjun beats Karan by 11 metres.
- Karan and Arjun reach the finishing line simultaneously.
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The Correct Option is A
Solution and Explanation
Step 1: Speed ratio from race 1:
When Karan finishes 100 m, Arjun has run 90 m (Karan wins by 10 m). Same time, so Karan : Arjun speeds = 100 : 90 = 10 : 9.
Step 2: Second race:
Karan must now run 110 m, Arjun 100 m. Let speeds be 10v and 9v. Karan's time = 110/(10v) = 11/v. Arjun's time = 100/(9v) = 11.11/v.
Step 3: Compare:
Karan's time (11/v) is less than Arjun's (11.11/v), so Karan wins. When Karan finishes (time 11/v), Arjun has run 9v x 11/v = 99 m, i.e. he is 1 m short of the finish line.
Step 4: Conclusion:
Karan beats Arjun by 1 metre.
Final Answer:
The correct option is (1): Karan beats Arjun by 1 metre.
When Karan finishes 100 m, Arjun has run 90 m (Karan wins by 10 m). Same time, so Karan : Arjun speeds = 100 : 90 = 10 : 9.
Step 2: Second race:
Karan must now run 110 m, Arjun 100 m. Let speeds be 10v and 9v. Karan's time = 110/(10v) = 11/v. Arjun's time = 100/(9v) = 11.11/v.
Step 3: Compare:
Karan's time (11/v) is less than Arjun's (11.11/v), so Karan wins. When Karan finishes (time 11/v), Arjun has run 9v x 11/v = 99 m, i.e. he is 1 m short of the finish line.
Step 4: Conclusion:
Karan beats Arjun by 1 metre.
Final Answer:
The correct option is (1): Karan beats Arjun by 1 metre.
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