There are two concentric circular tracks of radii 100 m and 102 m, respectively. A runs on the inner track and goes once round on the inner track in 1 min 30 sec, while B runs on the outer track in 1 min 32 sec. Who runs faster?

Options

A. Both A and B are equal
B. A
C. B
D. None of these

Answer

To determine who runs faster between A and B on their respective circular tracks, we will follow these steps:

### Step 1: Calculate the Circumference of Each Track
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

**For A (Inner Track):**
- Radius \( r_A = 100 \) m
\[ C_A = 2 \pi (100) = 200\pi \approx 628 \text{ m} \]

**For B (Outer Track):**
- Radius \( r_B = 102 \) m
\[ C_B = 2 \pi (102) = 204\pi \approx 640.8 \text{ m} \]

### Step 2: Convert Time Taken into Seconds
- A takes 1 minute 30 seconds to complete one round:
\[ \text{Time}_A = 1 \times 60 + 30 = 90 \text{ seconds} \]

- B takes 1 minute 32 seconds to complete one round:
\[ \text{Time}_B = 1 \times 60 + 32 = 92 \text{ seconds} \]

### Step 3: Calculate the Speed of Each Runner
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

**For A:**
\[ \text{Speed}_A = \frac{C_A}{\text{Time}_A} = \frac{628}{90} \approx 6.98 \text{ m/s} \]

**For B:**
\[ \text{Speed}_B = \frac{C_B}{\text{Time}_B} = \frac{640.8}{92} \approx 6.96 \text{ m/s} \]

### Step 4: Compare the Speeds
Now we compare the speeds calculated:
- Speed of A: \( 6.98 \text{ m/s} \)
- Speed of B: \( 6.96 \text{ m/s} \)

Since \( 6.98 \text{ m/s} > 6.96 \text{ m/s} \), A runs faster than B.

### Conclusion
A runs faster than B.

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