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. 0.042361111111111
B. 1:5
C. 0.045138888888889
D. 0.088194444444444

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Fraction
Let the numerator of the fraction be \( N \) and the denominator be \( D \). According to the problem, the ratio of the numerator to the denominator is given as:
\[ \frac{N}{D} = \frac{1}{5} \]
This implies that:
\[ N = 1k \quad \text{and} \quad D = 5k \]
for some constant \( k \).

### Step 2: Add Values to the Numerator and Denominator
Next, we add \( x \) to the numerator and \( 5x \) to the denominator. The new fraction becomes:
\[ \frac{N + x}{D + 5x} = \frac{1k + x}{5k + 5x} \]

### Step 3: Simplify the New Fraction
Now, we simplify the new fraction:
\[ \frac{N + x}{D + 5x} = \frac{k + x}{5k + 5x} \]
We can factor out a 5 from the denominator:
\[ = \frac{k + x}{5(k + x)} \]

### Step 4: Determine the New Ratio
The new fraction simplifies to:
\[ \frac{k + x}{5(k + x)} = \frac{1}{5} \]
This shows that the ratio of the new fraction remains \( \frac{1}{5} \).

### Conclusion
Thus, the ratio of the new fraction is still:
\[ \frac{1}{5} \]