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?
Step-by-step Solution:
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.