A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is :

Options

A. 25 min
B. 20 min
C. 50 min
D. 100 min

Answer

To solve the problem, we need to find out how long it will take A to go around a new circular path after the diameter has been increased to 10 times the original diameter. Let's break it down step by step.

### Step 1: Determine the original diameter and circumference
1. A can go around the original circular path 8 times in 40 minutes.
2. The total distance covered in 8 rounds is equal to 8 times the circumference of the circle.
3. Let the original diameter be \( d \). The circumference \( C \) of the circle is given by:
\[ C = \pi d \]
4. Therefore, the total distance covered in 8 rounds is:
\[ \text{Total distance} = 8C = 8(\pi d) \]

### Step 2: Calculate the speed of A
1. The time taken to cover this distance is 40 minutes.
2. The speed \( S \) of A can be calculated as:
\[ S = \frac{\text{Total distance}}{\text{Time}} = \frac{8(\pi d)}{40} = \frac{\pi d}{5} \text{ (in units of distance per minute)} \]

### Step 3: Determine the new diameter and circumference
1. The new diameter is 10 times the original diameter:
\[ \text{New diameter} = 10d \]
2. The new circumference \( C' \) of the circle is:
\[ C' = \pi \times \text{New diameter} = \pi (10d) = 10\pi d \]

### Step 4: Calculate the time taken to go around the new path once
1. The time taken \( T' \) to go around the new path once at the same speed \( S \) is given by:
\[ T' = \frac{\text{New circumference}}{S} = \frac{10\pi d}{\frac{\pi d}{5}} \]
2. Simplifying this:
\[ T' = 10\pi d \times \frac{5}{\pi d} = 10 \times 5 = 50 \text{ minutes} \]

### Conclusion
Thus, the time required by A to go around the new path once is **50 minutes**.

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