By what number must a given number be multiplied to increase it by `12%` ?

Answer

To solve the problem of determining by what number a given number must be multiplied to increase it by 12%, we can follow these steps:

### Step-by-Step Solution:

1. **Let the original number be X.**
- We start by defining the original number as \( X \).

2. **Calculate the increase of 12% of X.**
- To find 12% of \( X \), we use the formula for percentage:
\[ 12\% \text{ of } X = \frac{12}{100} \times X = \frac{12X}{100} \]

3. **Determine the new number after the increase.**
- The new number after increasing \( X \) by 12% is:
\[ \text{New number} = X + \frac{12X}{100} \]
- We can combine the terms:
\[ \text{New number} = X + \frac{12X}{100} = \frac{100X}{100} + \frac{12X}{100} = \frac{112X}{100} \]

4. **Simplify the expression for the new number.**
- We can simplify \( \frac{112X}{100} \) by dividing both the numerator and the denominator by 4:
\[ \frac{112X}{100} = \frac{28X}{25} \]

5. **Determine the multiplication factor.**
- To find the number by which \( X \) must be multiplied to get the new number, we set up the equation:
\[ \text{New number} = \text{Original number} \times \text{Multiplication factor} \]
- This gives us:
\[ \frac{28X}{25} = X \times \text{Multiplication factor} \]
- Dividing both sides by \( X \) (assuming \( X \neq 0 \)):
\[ \frac{28}{25} = \text{Multiplication factor} \]

6. **Conclusion.**
- Therefore, the number by which the original number must be multiplied to increase it by 12% is:
\[ \frac{28}{25} \]

### Final Answer:
The given number should be multiplied by \( \frac{28}{25} \) to increase it by 12%.

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