Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 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?

The correct answer is 4.8 km.

Let's break this problem down step by step.

Step 1: Understand the Setup
Anil, Sunil, and Ravi all start from the same point on a circular track of length 3 km, running clockwise. Their speeds are:

• Anil: 15 km/hr
• Sunil: 10 km/hr
• Ravi: 8 km/hr

Step 2: Determine when each runner returns to the starting point
A runner returns to the starting point every time they complete a full lap (3 km). The time to complete one lap is:

Time for Anil to complete one lap = $\frac{3}{15}$ = $\frac{1}{5}$ hr

Time for Sunil to complete one lap = $\frac{3}{10}$ hr

So Anil is at the starting point at every multiple of $\frac{1}{5}$ hr, and Sunil is at the starting point at every multiple of $\frac{3}{10}$ hr.

Step 3: Find when Anil and Sunil are BOTH at the starting point for the first time
We need the LCM (Least Common Multiple) of $\frac{1}{5}$ and $\frac{3}{10}$.

The formula for LCM of fractions is:

$\text{LCM}=\frac{\text{LCM of numerators}}{\text{GCD of denominators}}$

• LCM of numerators (1, 3) = 3
• GCD of denominators (5, 10) = 5

LCM = $\frac{3}{5}$ hr

Verification:
At time $t=\frac{3}{5}$ hr:
• Anil completes: $\frac{3/5}{1/5}=3$ laps ✓ (back at start)
• Sunil completes: $\frac{3/5}{3/10}=2$ laps ✓ (back at start)

Step 4: Calculate the distance Ravi covers in this time

Distance = Speed × Time = $8\times \frac{3}{5}$ = $\frac{24}{5}$ = 4.8 km

Therefore, when Anil and Sunil meet for the first time at the starting point (after $\frac{3}{5}$ hr = 36 minutes), Ravi will have run 4.8 km.