A man walks with speed 15 km/hr instead of 12 km/hr and covers 20 km more distance. Find the distance covered by him with speed 15 km/hr.

Options

A. 50 km
B. 60 km
C. 70 km
D. None of these

Answer

To solve the problem, we need to find the distance covered by the man when he walks at a speed of 15 km/hr. We will use the relationship between speed, distance, and time.

### Step-by-Step Solution:

1. **Let the distance covered at 12 km/hr be \( D \) km.**
- When he walks at 12 km/hr, he covers a distance \( D \).

2. **Calculate the time taken to cover distance \( D \) at 12 km/hr.**
- Time taken \( T_1 = \frac{D}{12} \) hours.

3. **When he walks at 15 km/hr, he covers 20 km more distance.**
- Therefore, the distance covered at 15 km/hr is \( D + 20 \) km.

4. **Calculate the time taken to cover distance \( D + 20 \) at 15 km/hr.**
- Time taken \( T_2 = \frac{D + 20}{15} \) hours.

5. **Since the time taken to cover the distance at both speeds is the same, we can set the two time equations equal to each other:**
\[ \frac{D}{12} = \frac{D + 20}{15} \]

6. **Cross-multiply to eliminate the fractions:**
\[ 15D = 12(D + 20) \]

7. **Distribute the 12 on the right side:**
\[ 15D = 12D + 240 \]

8. **Rearrange the equation to isolate \( D \):**
\[ 15D - 12D = 240 \]
\[ 3D = 240 \]

9. **Solve for \( D \):**
\[ D = \frac{240}{3} = 80 \text{ km} \]

10. **Now, calculate the distance covered at 15 km/hr:**
\[ \text{Distance at 15 km/hr} = D + 20 = 80 + 20 = 100 \text{ km} \]

### Final Answer:
The distance covered by him with a speed of 15 km/hr is **100 km**.