Multiple choice

Three persons $A, B$ and $C$ run along a circular path $12$ km long. They start their race along the same point at the same time with a speed of $3$ km/hr, $7$ km/hr and $13$ km/hr respectively. After what time will they meet again?

  1. $16$ hours
  2. $24$ hours
  3. $9$ hours
  4. $12$ hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Time taken for one lap is distance/speed. A: 12/3 = 4 hrs, B: 12/7 hrs, C: 12/13 hrs. They meet at the LCM of (4, 12/7, 12/13) = LCM(4, 12, 12) / HCF(1, 7, 13) = 12 / 1 = 12 hours.

AI explanation

The times taken for one full round are 4/3, 12/7, and 12/13 hours. The required meeting time is the LCM of these fractions, given by LCM of numerators divided by HCF of denominators. This simplifies to 12/1 hours, or 12 hours.

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