Pihu and Aayu are running on a circular track of diameter 28 m . Speed of Pihu is 48m/s and that of Aayu is 40 m/s . They start from the same point at the same time in the same direction . When will they meet again for the first time ?

Options

A. 8 seconds
B. 11 seconds
C. 13 seconds
D. 14 seconds

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Circumference of the Circular Track
The formula for the circumference \( C \) of a circle is given by:
\[ C = \pi \times d \]
where \( d \) is the diameter.

Given that the diameter \( d = 28 \) m, we can substitute this value into the formula:
\[ C = \pi \times 28 \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = \frac{22}{7} \times 28 = 88 \text{ m} \]

### Step 2: Determine the Speeds of Pihu and Aayu
Pihu's speed \( v_P = 48 \) m/s and Aayu's speed \( v_A = 40 \) m/s.

### Step 3: Calculate the Relative Speed
Since both are running in the same direction, the relative speed \( v_{rel} \) is calculated as:
\[ v_{rel} = v_P - v_A = 48 \text{ m/s} - 40 \text{ m/s} = 8 \text{ m/s} \]

### Step 4: Calculate the Time Taken to Meet Again
To find out when they will meet again, we need to determine how long it will take for Pihu to gain a full lap (the circumference) over Aayu. The time \( t \) can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{C}{v_{rel}} \]
Substituting the values we have:
\[ t = \frac{88 \text{ m}}{8 \text{ m/s}} = 11 \text{ seconds} \]

### Conclusion
Pihu and Aayu will meet again for the first time after **11 seconds**.

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