Karan and Arjun run a 100 metres 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?
1. Find the Ratio of Speeds from the First Race - In the first 100 m race, Karan beats Arjun by 10 metres.
- This means that in the same amount of time, when Karan runs 100 m, Arjun only runs (100 - 10) = 90 m.
- The ratio of distances covered is equal to the ratio of their speeds.
- Ratio of Speeds (Karan : Arjun) = 100 : 90, which simplifies to 10 : 9.
2. Analyze the Second Race Setup - The race is to a 100 m finishing line.
- Karan starts 10 m behind the starting line, so the total distance he must run is 100 m + 10 m = 110 m.
- Arjun starts at the regular starting line, so he must run 100 m.
3. Determine the Winner and the Margin - Let's find out where Arjun is when Karan finishes his 110 m run. Since their speed ratio is 10:9, the distance they cover will also be in that ratio.
- Distance Arjun runs = (9/10) × (Distance Karan runs)
- Distance Arjun runs = (9/10) × 110 m = 99 meters.
- So, by the time Karan reaches the finishing line, Arjun has only covered 99 meters of his 100-meter race.
- Therefore, Karan beats Arjun by 100 m - 99 m = 1 metre.
Final Answer: Karan beats Arjun by 1 metre.
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