Circular race meeting point

CAT 2020 Slot 3 · QA · Medium · Circular races

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Anil, Sunil, and Ravi run along a circular path of length 3 km3\text{ km}, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr15\text{ km/hr}, 10 km/hr10\text{ km/hr}, and 8 km/hr8\text{ km/hr}, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

  1. A.

    4.6

  2. B.

    4.2

  3. C.

    4.8

  4. D.

    5.2

Answer

C

Explanation

Time taken by Anil to complete 1 lap = 315=15 hr\frac{3}{15} = \frac{1}{5}\text{ hr}. Time taken by Sunil to complete 1 lap = 310 hr\frac{3}{10}\text{ hr}.

Anil and Sunil meet at the starting point at intervals of LCM(15,310)=LCM(1,3)HCF(5,10)=35 hr=0.6 hours\text{LCM}\left(\frac{1}{5}, \frac{3}{10}\right) = \frac{\text{LCM}(1, 3)}{\text{HCF}(5, 10)} = \frac{3}{5}\text{ hr} = 0.6\text{ hours}.

Distance run by Ravi in 0.6 hours=8×0.6=4.8 km0.6\text{ hours} = 8 \times 0.6 = 4.8\text{ km}.

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