Question:medium

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

Step 1: Read off the speed ratios from the given gaps.
A beats B by 20 m in a 100 m race, so when A covers 100 m, B covers \( 100-20=80 \) m. B beats C by 5 m in a 100 m race, so when B covers 100 m, C covers \( 100-5=95 \) m.

Step 2: Find C's distance when B has run 80 m.
Since B and C cover distances in the ratio \( 100:95 \) over any equal time, when B covers 80 m, C covers: \[ 80 \times \frac{95}{100} = 76 \text{ m} \]

Step 3: Compare with A's finishing distance.
When A finishes 100 m, B has covered 80 m, and in that same time C has covered 76 m. So the gap between A and C is \( 100 - 76 = 24 \) m.

Step 4: Final Answer.
Chaining the two given gaps together shows A finishes 24 m ahead of C. \[ \boxed{24 \text{ m}} \]
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Approach Solution -2

Since A beats B by a 20% margin and B beats C by a 5% margin over the same 100 m distance, the overall margin by which A beats C can be found using the formula for combining two successive percentage decreases: net decrease \( = a+b-\frac{ab}{100} \), where \( a \) and \( b \) are the two individual percentage margins.

  1. 26 meters: Substituting \( a=20 \) and \( b=5 \) gives \( 20+5-\frac{20\times5}{100}=25-1=24 \), a combined margin that does not equal 26.
  2. 25 meters: The same substitution gives exactly 24, not 25, so this option is a percentage point off from the true combined margin.
  3. 24 meters: The formula \( 20+5-\frac{20\times5}{100}=24 \) matches this option precisely, since B's 20% deficit against A and C's 5% deficit against B do not simply add, they combine with a small overlap correction of \( \frac{20\times5}{100}=1 \).
  4. 22 meters: This value is lower than the 24 the combination formula actually produces, so it does not fit.

Combining the two percentage margins with the correction term for their overlap gives a net margin of exactly 24%, meaning C is 24 m behind when A finishes the 100 m race.

Therefore, the correct answer is 24 meters.

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