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:
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Chain race problems can be solved by converting each race result into speed ratios and multiplying them.
Updated On: Jul 15, 2026
- 26 meters
- 25 meters
- 24 meters
- 22 meters
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The Correct Option is C
Approach Solution - 1
Step 1: A beats B by 20 m means: When A runs 100 m, B runs 80 m.
Step 2: B beats C by 5 m means: When B runs 100 m, C runs 95 m.
Step 3: In A’s 100 m run, B runs 80 m. In that time, C runs:
$95/100 \times 80 = 76$ m.
Step 4: Hence A beats C by:
$100 - 76 = 24$ m.
Step 2: B beats C by 5 m means: When B runs 100 m, C runs 95 m.
Step 3: In A’s 100 m run, B runs 80 m. In that time, C runs:
$95/100 \times 80 = 76$ m.
Step 4: Hence A beats C by:
$100 - 76 = 24$ m.
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Approach Solution -2
The question gives two separate 100 meter races and asks how far A beats C by. We can find the speed ratios of A, B and C, combine them, then check which option matches.
- 26 meters: This would mean C covers only 74 m when A covers 100 m. Combining the ratios A:B = 100:80 and B:C = 100:95 gives A:B:C = 100:80:76, so C should cover 76 m, not 74 m. This does not match.
- 25 meters: This would mean C covers 75 m when A covers 100 m, which is 1 m short of the 76 m given by the combined ratio. This does not match.
- 24 meters: This would mean C covers 76 m when A covers 100 m. Combining the ratios, \( \text{A:B:C} = 100 : 80 : \left(80 \times \tfrac{95}{100}\right) = 100:80:76 \), which matches exactly.
- 22 meters: This would mean C covers 78 m when A covers 100 m, which does not match the combined ratio 100:80:76.
The combined speed ratio A:B:C = 100:80:76 shows that when A covers 100 m, C covers only 76 m, so A beats C by \( 100-76=24 \) m.
Therefore, the correct answer is 24 meters.
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Approach Solution -3
We can work this out using speeds and times instead of combining ratios directly. Imagine A takes exactly 1 second to run 100 m. Since A beats B by 20 m in that time, B covers only 80 m in that same 1 second, so B's speed is 80 m per second on this scale. We can now check each option by seeing whether it is consistent with C's speed as derived from B's own 100 m race.
- 26 meters: This would mean C covers only \( 100-26=74 \) m in A's 1 second, giving C a speed of 74 m/s. But B takes \( 100/80=1.25 \) seconds to run 100 m, and in that time C runs 95 m (since B beats C by 5 m), so C's true speed is \( 95/1.25=76 \) m/s, not 74. This option does not fit.
- 25 meters: This implies C covers 75 m in A's 1 second, a speed of 75 m/s, still short of the required 76 m/s derived from B's race.
- 24 meters: This implies C covers \( 100-24=76 \) m in A's 1 second, a speed of exactly 76 m/s, matching precisely the speed derived from B's own 100 m race against C.
- 22 meters: This implies C covers 78 m in A's 1 second, a speed of 78 m/s, higher than the required 76 m/s, so this option overshoots.
C's actual speed, worked out from B's race, is 76 m/s on this timescale, which means C covers only 76 m while A covers 100 m, so A beats C by 24 m.
Therefore, the correct answer is 24 meters.
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