To determine when the three runners (Anisha, Bimala, and Chetana) will meet again after starting from the same point, we need to calculate the time after which they are all at the same position along the circular path.

Step 1: Time for one complete round

First, we calculate the time taken by each runner to complete one round (12 km) based on their respective speeds:

• Anisha's time = $\frac{\text{Distance}}{\text{Speed}} = \frac{12 \text{ km}}{5 \text{ km/hr}} = 2.4 \text{ hours}$
• Bimala's time = $\frac{\text{Distance}}{\text{Speed}} = \frac{12 \text{ km}}{7 \text{ km/hr}} = \frac{12}{7} \approx 1.714 \text{ hours}$
• Chetana's time = $\frac{\text{Distance}}{\text{Speed}} = \frac{12 \text{ km}}{13 \text{ km/hr}} \approx 0.923 \text{ hours}$

Step 2: Find the Least Common Multiple (LCM) of these times

The time after which all runners meet again will be the Least Common Multiple (LCM) of their individual times.

The times in fractional form are:

• $2.4 = \frac{12}{5}$ hours
• $\frac{12}{7}$ hours
• $\frac{12}{13}$ hours

To find the LCM, we use the LCM of the denominators 5, 7, and 13, as the numerators (12) are the same.

The LCM of 5, 7, and 13 is $5 \times 7 \times 13 = 455$.

Step 3: Calculate the LCM of the times

Thus, the LCM of the times in terms of hours will be:

[ \frac{12 \times 455}{\text{LCM of (denominators)}} = \frac{12 \times 455}{5 \times 7 \times 13} = n ... ]