A boy added all natural numbers from 1 to 20. However he added one number twice, due to which the sum becomes 215. What is the number which he added twice?

Options

A. 5
B. 7
C. 11
D. 15

Answer

To solve the problem, we need to find the natural number that was added twice, which caused the total sum to be 215 instead of the correct sum of all natural numbers from 1 to 20.

### Step 1: Calculate the sum of natural numbers from 1 to 20.
The formula for the sum of the first n natural numbers is given by:

\[ S_n = \frac{n(n + 1)}{2} \]

In this case, \( n = 20 \).

\[ S_{20} = \frac{20(20 + 1)}{2} = \frac{20 \times 21}{2} = \frac{420}{2} = 210 \]

### Step 2: Set up the equation with the added number.
Let \( x \) be the number that was added twice. The equation for the total sum becomes:

\[ 210 + x = 215 \]

### Step 3: Solve for \( x \).
To find \( x \), we rearrange the equation:

\[ x = 215 - 210 \]
\[ x = 5 \]

### Conclusion:
The number that was added twice is **5**.

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