A man walks in an increasing pattern, covering 1 km on the first day, 2 km on the second day, 3 km on the third day, and so on. What is the total distance he covers in 10 days?

Introduction / Context:
This question checks your understanding of arithmetic progressions and summation of consecutive natural numbers. The daily walking distances form a simple increasing sequence where each term increases by a fixed amount. Recognizing this pattern helps you use a direct formula instead of adding each day manually.

Given Data / Assumptions:
Day 1 distance = 1 km.
Day 2 distance = 2 km.
Day 3 distance = 3 km, and the pattern continues with an increase of 1 km per day.
The man follows this pattern for 10 consecutive days.
We assume there are no breaks and no changes in the pattern during these 10 days.

Concept / Approach:
The distances walked each day form an arithmetic progression with first term a = 1, common difference d = 1, and number of terms n = 10. The sum of the first n natural numbers is a well known result: n * (n + 1) / 2. Using this formula makes the calculation fast and accurate. Applying it correctly is a common skill expected in aptitude exams.

Step-by-Step Solution:
Step 1: List the daily distances: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 km.Step 2: Recognize that this is the sequence of the first 10 natural numbers.Step 3: Use the formula for the sum of the first n natural numbers: Sum = n * (n + 1) / 2.Step 4: Substitute n = 10: Sum = 10 * (10 + 1) / 2.Step 5: Sum = 10 * 11 / 2 = 110 / 2.Step 6: Therefore, Sum = 55 km.Step 7: This is the total distance walked in 10 days.

Verification / Alternative check:
You can check by pairing terms from the beginning and end of the sequence: (1 + 10) + (2 + 9) + (3 + 8) + (4 + 7) + (5 + 6). Each pair sums to 11, and there are 5 such pairs, so total distance = 5 * 11 = 55 km. This alternative method agrees with the formula based approach and confirms that the total distance is correct.

Why Other Options Are Wrong:
40 km and 45 km underestimate the sum because they correspond to stopping the pattern earlier than 10 days or miscalculating the series.
50 km arises if someone mistakenly uses 10 * 10 / 2 or forgets to add the last term correctly, which is a common error.
58 km is an overestimate and does not match the sum of the exact daily distances from 1 to 10.

Common Pitfalls:
A common mistake is to assume that since the last term is 10 km, the average is 10 / 2 = 5 and then incorrectly multiply by 10 without following the proper formula. Another issue is adding the numbers quickly in the mind and missing one or more terms. Remembering and correctly applying the arithmetic progression sum formula is a reliable way to avoid these errors.

Final Answer:
The man covers a total distance of 55 km in 10 days.