A man walks 1 km. on 1st day, 2 km. on 2nd day, 3 km, on 3rd day and so on. The total distance the man covers in 10 days is :

Options

A. 40 km
B. 50 km
C. 55 km
D. 58 km

Answer

To find the total distance covered by the man in 10 days, we can follow these steps:

1. **Identify the pattern of distance walked each day**:
- On the 1st day, he walks 1 km.
- On the 2nd day, he walks 2 km.
- On the 3rd day, he walks 3 km.
- This pattern continues until the 10th day, where he walks 10 km.

2. **List the distances covered each day**:
- The distances for the 10 days are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 km.

3. **Recognize that this is an arithmetic series**:
- The distances form an arithmetic series where the first term \(a = 1\) km, the last term \(l = 10\) km, and the number of terms \(n = 10\).

4. **Use the formula for the sum of the first n natural numbers**:
- The formula for the sum \(S_n\) of the first \(n\) natural numbers is given by:
\[ S_n = \frac{n(n + 1)}{2} \]
- Here, \(n = 10\).

5. **Substitute the value of n into the formula**:
- Plugging in the value:
\[ S_{10} = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = \frac{110}{2} = 55 \]

6. **Conclusion**:
- Therefore, the total distance covered by the man in 10 days is **55 km**.