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

$5.2$

$4.6$

$4.8$

$4.2$

✅ Correct Option: 3

They meet at the starting point only when both have completed whole laps at the same time.

Time for one complete lap using Distance ÷ Speed:

Anil:

$\dfrac{3}{15} = \dfrac{1}{5}$ hours per lap

Sunil:

$\dfrac{3}{10}$ hours per lap

Ravi:

$\dfrac{3}{8}$ hours per lap

To find when Anil and Sunil both finish whole laps together, we need the LCM of their lap times.

For fractions:

$\text{LCM}\left(\dfrac{a}{b}, \dfrac{c}{d}\right) = \dfrac{\text{LCM}(a,c)}{\text{GCD}(b,d)}$

For $\dfrac{1}{5}$ and $\dfrac{3}{10}$ :

$\text{LCM}(1,3) = 3$ and $\text{GCD}(5,10) = 5$

Therefore:

$\text{LCM}\left(\dfrac{1}{5}, \dfrac{3}{10}\right) = \dfrac{3}{5}$ hours

Ravi's distance in $\dfrac{3}{5}$ hours:

Distance $=$ Speed $\times$ Time

$= 8 \times \dfrac{3}{5} = \dfrac{24}{5} = 4.8$ km

Answer: $4.8$ km

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