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:

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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: In the same time A runs 100 m, B runs 80 m, since A beats B by 20 m. So B's distance is 80 percent of A's distance for equal time.

Step 2: In the same time B runs 100 m, C runs 95 m, since B beats C by 5 m. So C's distance is 95 percent of B's distance for equal time.

Step 3: Combining, C's distance is 95 percent of 80 percent of A's distance, which is \( 0.95 \times 0.80 = 0.76 \), or 76 percent. So when A runs 100 m, C runs \( 0.76 \times 100 = 76 \) m.

Step 4: A beats C by \( 100-76=24 \) m.
\[ \boxed{24 \text{ m}} \]
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Approach Solution -2

To avoid fractions altogether, scale the race up to a length of 400 m, four times the original, so all the given head starts scale up by the same factor of 4. We can then check each option by comparing it against the head start computed on this larger, whole-number scale.

  1. 26 meters: Scaled up, this would be a head start of \( 26 \times 4=104 \) m in the 400 m race. On the 400 m scale, A beating B by 20 m becomes A beating B by 80 m, and B beating C by 5 m becomes B beating C by 20 m; when B covers \( 400-80=320 \) m, which is \( 320/400=0.8 \) of B's own race, C covers \( 0.8 \times (400-20)=0.8 \times 380=304 \) m, so A beats C by \( 400-304=96 \) m, not 104 m.
  2. 25 meters: Scaled up, this is \( 25 \times 4=100 \) m, which does not match the computed 96 m gap on the 400 m scale.
  3. 24 meters: Scaled up, this is \( 24 \times 4=96 \) m, matching exactly the gap of 96 m worked out on the 400 m scale.
  4. 22 meters: Scaled up, this is \( 22 \times 4=88 \) m, which does not match the computed 96 m gap either.

Working the race out on a scaled-up 400 m track avoids fractional distances and confirms A beats C by 96 m on that scale, which is 24 m on the original 100 m track.

Therefore, the correct answer is 24 meters.

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