If a man covers `4/5th` part of a circular track in m minutes, at the same rate, how many minutes does he take to complete one revolution around the entire track?

Options

A. `(5m)/4` minutes
B. `(4m)/5` minutes
C. `5/(4m)` minutes
D. `m/4` minutes

Answer

To solve the problem, we need to determine how long it takes for the man to complete one full revolution of the circular track given that he covers \( \frac{4}{5} \) of the track in \( m \) minutes.

### Step-by-Step Solution:

1. **Understand the distance covered**: The man covers \( \frac{4}{5} \) of the circular track in \( m \) minutes.

2. **Determine the time for the full track**: Since \( \frac{4}{5} \) of the track takes \( m \) minutes, we can find the time for the entire track (1 full revolution) by setting up a proportion.

The relationship can be expressed as:
\[ \text{Time for full track} = \frac{\text{Time for } \frac{4}{5} \text{ track}}{\frac{4}{5}} = \frac{m}{\frac{4}{5}} \]

3. **Simplify the expression**: To simplify \( \frac{m}{\frac{4}{5}} \), we multiply \( m \) by the reciprocal of \( \frac{4}{5} \):
\[ \frac{m}{\frac{4}{5}} = m \times \frac{5}{4} = \frac{5m}{4} \]

4. **Conclusion**: Therefore, the time taken to complete one full revolution around the circular track is \( \frac{5m}{4} \) minutes.

### Final Answer:
The man takes \( \frac{5m}{4} \) minutes to complete one revolution around the entire track.

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