From a bus terminal buses start at an interval of 10 minutes. A man coming towards the bus terminal meet the buses at an interval of 8 minutes. If the speed of bus is 24 km/hr then find the speed of man.

Options

A. 6 km
B. 5 km
C. 4 km
D. 3 km

Answer

To solve the problem, we need to find the speed of the man (let's denote it as \( x \) km/hr) based on the information given about the buses and their intervals.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- Buses leave the terminal every 10 minutes.
- The man meets the buses every 8 minutes.
- The speed of the bus is 24 km/hr.

2. **Convert Time Intervals to Hours:**
- The time interval between buses is 10 minutes, which is \( \frac{10}{60} = \frac{1}{6} \) hours.
- The time interval at which the man meets the buses is 8 minutes, which is \( \frac{8}{60} = \frac{2}{15} \) hours.

3. **Calculate the Distance Traveled by the Bus:**
- In the time interval of 10 minutes, the distance traveled by the bus can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Therefore, the distance traveled by the bus in \( \frac{1}{6} \) hours is:
\[ \text{Distance}_{\text{bus}} = 24 \times \frac{1}{6} = 4 \text{ km} \]

4. **Calculate the Distance Traveled by the Man:**
- In the time interval of 8 minutes, the distance traveled by the man can be calculated as:
\[ \text{Distance}_{\text{man}} = \text{Speed}_{\text{man}} \times \text{Time} \]
- Therefore, the distance traveled by the man in \( \frac{2}{15} \) hours is:
\[ \text{Distance}_{\text{man}} = x \times \frac{2}{15} \]

5. **Setting Up the Equation:**
- Since the man meets the bus, the distances traveled by both the bus and the man must be equal:
\[ 4 = x \times \frac{2}{15} \]

6. **Solving for the Speed of the Man:**
- Rearranging the equation gives:
\[ x = 4 \times \frac{15}{2} = 4 \times 7.5 = 30 \text{ km/hr} \]

7. **Final Calculation:**
- Therefore, the speed of the man is:
\[ x = 30 \text{ km/hr} \]

### Conclusion:
The speed of the man is **30 km/hr**.