Question:
In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?
In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?
Updated On: Jul 30, 2025
- 1200
- 1900
- 3100
- 1500
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The Correct Option is B
Solution and Explanation
To determine by how many meters A beats C, we first need to analyze the relationships based on their speeds and time taken. Given:
- A beats B by 1 km, meaning that when A finishes 10 km, B finishes 9 km.
- B beats C by 1 km, meaning that when B finishes 10 km, C finishes 9 km.
We can express time as distance/speed. Since all runners run at uniform speeds for the same amount of race time:
- Let the speed of A be sA. Then the time for A to complete 10 km is 10/sA.
- Let the speed of B be sB. The time required by B for 9 km (B's position when A finishes) is 9/sB = 10/sA. Therefore, sB = (9/10) × sA.
- Let the speed of C be sC. The time required by C for 9 km (C's position when B finishes 10 km) is 9/sC = 10/sB. Therefore, sC = (9/10) × sB = (9/10)² × sA.
We want to find how much distance C covers in the time A finishes 10 km:
- Time taken by A to complete 10 km: 10/sA.
- Distance C runs in this time: 10 × sC/sA.
- Substitute sC: 10 × [(9/10)² × sA]/sA = 10 × (81/100) = 8.1 km.
A beats C by the difference between 10 km and 8.1 km:
- Distance A beats C: 10 km - 8.1 km = 1.9 km which is 1900 meters.
The correct answer is thus: 1900 meters.
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