Find a number :
Which when increased by `10%` becomes 66.

Answer

To find the number which, when increased by 10%, becomes 66, we can follow these steps:

### Step-by-Step Solution:

1. **Let the number be \( x \)**:
- We start by defining the unknown number as \( x \).

2. **Set up the equation**:
- According to the problem, when \( x \) is increased by 10%, it becomes 66. This can be expressed mathematically as:
\[ x + 10\% \text{ of } x = 66 \]

3. **Convert 10% to a fraction**:
- 10% can be written as \( \frac{10}{100} \) or \( \frac{1}{10} \). Therefore, \( 10\% \text{ of } x \) is:
\[ \frac{10}{100} \times x = \frac{x}{10} \]

4. **Rewrite the equation**:
- Substitute \( 10\% \text{ of } x \) back into the equation:
\[ x + \frac{x}{10} = 66 \]

5. **Combine the terms**:
- To combine \( x \) and \( \frac{x}{10} \), we need a common denominator. The common denominator is 10:
\[ \frac{10x}{10} + \frac{x}{10} = 66 \]
- This simplifies to:
\[ \frac{10x + x}{10} = 66 \]
- Which further simplifies to:
\[ \frac{11x}{10} = 66 \]

6. **Solve for \( x \)**:
- To isolate \( x \), multiply both sides by 10:
\[ 11x = 66 \times 10 \]
- This gives:
\[ 11x = 660 \]
- Now, divide both sides by 11:
\[ x = \frac{660}{11} \]
- Calculating this gives:
\[ x = 60 \]

7. **Conclusion**:
- Therefore, the number is \( 60 \).