In a circular path of 600 m, Pankaj and Rohit start walking in opposite directions from the same point at the speeds of 2.85 m/s and 5.4 km/h, respectively. After how many minutes will they meet for the first time? (Rounded off to one decimal point)

The correct option is 2.3.

Step-by-step Explanation:

To find the time after which Pankaj and Rohit will meet for the first time, we can use the concept of relative speed for two objects moving in opposite directions along a circular track.

Step 1: Write down the given values and convert speeds to a common unit (meters per second, m/s).
Length of the circular path (Distance, $D$) = $600\text{m}$
Speed of Pankaj ($S_P$) = $2.85\text{m/s}$
Speed of Rohit ($S_R$) = $5.4\text{km/h}$

To convert Rohit's speed from km/h to m/s, we multiply by $\frac{5}{18}$:
$S_R=5.4\times \frac{5}{18}=0.3\times 5=1.5\text{m/s}$

Step 2: Calculate the relative speed.
Since they start from the same point and walk in opposite directions, their relative speed ($S_{\text{rel}}$) is the sum of their individual speeds:
$S_{\text{rel}}=S_P+S_R$
$S_{\text{rel}}=2.85+1.5=4.35\text{m/s}$

Step 3: Calculate the time taken to meet for the first time.
The time ($T$ in seconds) taken to meet for the first time is given by the formula:
$T=\frac{\text{Distance}}{\text{Relative Speed}}$
$T=\frac{600}{4.35}\text{seconds}$

Step 4: Convert the time into minutes and round off to one decimal point.
Since $1\text{minute}=60\text{seconds}$, we divide the time in seconds by $60$:
$T_{\text{minutes}}=\frac{600}{4.35\times 60}$
$T_{\text{minutes}}=\frac{10}{4.35}\approx 2.2988\text{minutes}$

Rounding to one decimal place, we get:
$T_{\text{minutes}}\approx 2.3\text{minutes}$

Therefore, Pankaj and Rohit will meet for the first time after 2.3 minutes.