Question:
In a 100 meters race, A beats B by 20 meters B beats C by 5 meters. In the same race, A beats C by:
In a 100 meters race, A beats B by 20 meters B beats C by 5 meters. In the same race, A beats C by:
Updated On: Aug 14, 2026
- 26 meters
- 25 meters
- 24 meters
- 22 meters
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The Correct Option is C
Approach Solution - 1
The correct option is (C): 24 meters.
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The question gives a 100 metre race where A beats B by 20 m and B beats C by 5 m, and asks by how much A beats C. Since the amount by which A beats C depends on how far C has run by the time A finishes, we can test each option by checking whether it matches C's position when A crosses the finish line.
- 26 meters: This would mean C has covered 74 m when A finishes. Working out C's actual distance from the given ratios does not produce this figure.
- 25 meters: This would mean C has covered 75 m when A finishes, which again does not match the distance implied by combining the two given race gaps.
- 24 meters: When A covers 100 m, B has covered only 80 m. When B covers 100 m, C covers 95 m, so B and C's speeds are in the ratio \( 100:95 \). At the moment A finishes, B has covered 80 m, so in that same time C covers \( 80 \times \frac{95}{100} = 76 \) m. This means C is 24 m behind A when A finishes, matching this option exactly.
- 22 meters: This would mean C has covered 78 m when A finishes, which is not consistent with the speed ratios derived from the two given gaps.
Chaining B's position when A finishes with C's position when B finishes shows C is exactly 24 m behind when A crosses the line.
Therefore, the correct answer is 24 meters.
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Approach Solution -3
The question describes a 100 m race in which A beats B by 20 m, and B beats C by 5 m, then asks by how much A beats C. Assigning A a concrete speed and working out actual times and speeds for each runner, rather than scaling ratios abstractly, traces exactly how far C has run when A crosses the line.
- 26 meters: Suppose A runs at 10 m/s, taking 10 seconds to finish the 100 m race. Since A beats B by 20 m, B has covered only 80 m in that same 10 seconds, giving B a speed of 8 m/s. Checking whether C is 26 m behind A at this pace does not match the numbers worked out from B and C's actual speeds below.
- 25 meters: Working through B and C's real speeds, as shown for the correct option below, does not produce a 25 m gap between A and C either.
- 24 meters: At B's speed of 8 m/s, B takes \( 100/8=12.5 \) seconds to finish 100 m. Since B beats C by 5 m over 100 m, C covers 95 m in those same 12.5 seconds, giving C a speed of \( 95/12.5=7.6 \) m/s. In A's actual finishing time of 10 seconds, C covers \( 7.6\times10=76 \) m, which is 24 m short of A's 100 m, matching this option exactly.
- 22 meters: The actual speeds worked out for B and C above do not support a 22 m gap between A and C either.
Assigning A a real speed and deriving B's and then C's actual speeds from the two given race gaps shows C covers only 76 m in the time A finishes, a 24 m shortfall.
Therefore, the correct answer is 24 meters.
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