The ratio of numerator to a denominator of a fraction is `1/5` when x and 5x are added to the numerator and denominator respectively to the given fraction then the ratio of the new fraction will be:

Options

A. `1:1`
B. `1:25`
C. `1:5`
D. `2:7`

Answer

To solve the problem step by step, we will follow the instructions given in the question regarding the fraction and the changes made to it.

### Step-by-Step Solution:

1. **Define the Fraction**:
Let the numerator be \( x \) and the denominator be \( y \). According to the problem, the ratio of the numerator to the denominator is \( \frac{1}{5} \).
\[ \frac{x}{y} = \frac{1}{5} \]

2. **Express the Denominator in Terms of the Numerator**:
From the ratio, we can express \( y \) in terms of \( x \):
\[ y = 5x \]

3. **Write the Original Fraction**:
Now, we can write the original fraction using the values of \( x \) and \( y \):
\[ \text{Original Fraction} = \frac{x}{5x} \]

4. **Add x and 5x to the Numerator and Denominator**:
According to the problem, we add \( x \) to the numerator and \( 5x \) to the denominator:
\[ \text{New Numerator} = x + x = 2x \]
\[ \text{New Denominator} = 5x + 5x = 10x \]

5. **Write the New Fraction**:
The new fraction after the additions is:
\[ \text{New Fraction} = \frac{2x}{10x} \]

6. **Simplify the New Fraction**:
We can simplify this new fraction:
\[ \frac{2x}{10x} = \frac{2}{10} = \frac{1}{5} \]

7. **Conclusion**:
The ratio of the new fraction remains the same as the original ratio:
\[ \text{Ratio of the new fraction} = \frac{1}{5} \]

### Final Answer:
The ratio of the new fraction is \( \frac{1}{5} \).

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