A boy added all natural numbers from 1 to 10, however he added one number twice due to which the sum became 58. What is the number which he added twice?

Options

A. 3
B. 4
C. 7
D. 8

Answer

To solve the problem step by step, we need to find out which natural number from 1 to 10 was added twice, resulting in a total sum of 58.

### Step 1: Calculate the sum of natural numbers from 1 to 10
The formula for the sum of the first n natural numbers is given by:
\[ S = \frac{n(n + 1)}{2} \]
For n = 10:
\[ S = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = 55 \]

**Hint:** Use the formula for the sum of the first n natural numbers to find the total sum without any duplicates.

### Step 2: Set up the equation for the sum with one number added twice
Let \( x \) be the number that was added twice. The new sum can be expressed as:
\[ 55 + x = 58 \]

**Hint:** Recognize that the total sum is the original sum plus the duplicated number.

### Step 3: Solve for \( x \)
Rearranging the equation gives:
\[ x = 58 - 55 \]
\[ x = 3 \]

**Hint:** Isolate \( x \) by subtracting the original sum from the total sum.

### Conclusion
The number that was added twice is **3**.

**Final Answer:** The number which he added twice is **3**.