Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?

Options

A. A) 27 sec
B. B) 31 sec
C. C) 23 sec
D. D) 29 sec

Answer

To solve the problem of when two persons running in opposite directions on a circular track will first meet, we can follow these steps:

### Step 1: Convert Speeds to the Same Unit
The speeds of the two persons are given in kilometers per hour (km/hr). We need to convert these speeds to meters per second (m/s) for easier calculations with the track length, which is in meters.

- Speed of Person A = 15 km/hr
- Speed of Person B = 25 km/hr

To convert km/hr to m/s, we use the conversion factor \( \frac{1000 \text{ m}}{3600 \text{ s}} \).

\[ \text{Speed of Person A in m/s} = 15 \times \frac{1000}{3600} = \frac{15000}{3600} = 4.17 \text{ m/s} \]

\[ \text{Speed of Person B in m/s} = 25 \times \frac{1000}{3600} = \frac{25000}{3600} = 6.94 \text{ m/s} \]

### Step 2: Calculate the Relative Speed
Since the two persons are running in opposite directions, we can find their relative speed by adding their speeds together.

\[ \text{Relative Speed} = \text{Speed of Person A} + \text{Speed of Person B} = 4.17 \text{ m/s} + 6.94 \text{ m/s} = 11.11 \text{ m/s} \]

### Step 3: Determine the Time to Meet
The time taken to meet for the first time can be calculated using the formula:

\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} \]

Here, the total distance is the length of the circular track, which is 300 meters.

\[ \text{Time} = \frac{300 \text{ m}}{11.11 \text{ m/s}} \approx 27 \text{ seconds} \]

### Final Answer
The two persons will meet for the first time after approximately **27 seconds**.

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