If the numerator of a fraction is increased by 200% and the denominator is increased by 400%, the resultant is `1 1/20`. What was the original fraction?

Options

A. `1 3/4`
B. `1 1/10`
C. `6/5`
D. `1 1/2`

Answer

To solve the problem, we need to find the original fraction given that the numerator is increased by 200% and the denominator is increased by 400%, resulting in the value of \(1 \frac{1}{20}\).

### Step-by-Step Solution:

1. **Define the Original Fraction**:
Let the original fraction be \(\frac{x}{y}\), where \(x\) is the numerator and \(y\) is the denominator.

2. **Calculate the Increased Numerator**:
If the numerator \(x\) is increased by 200%, the new numerator becomes:
\[ x + 200\% \text{ of } x = x + 2x = 3x \]

3. **Calculate the Increased Denominator**:
If the denominator \(y\) is increased by 400%, the new denominator becomes:
\[ y + 400\% \text{ of } y = y + 4y = 5y \]

4. **Set Up the Equation**:
The new fraction after the increases is:
\[ \frac{3x}{5y} \]
According to the problem, this fraction is equal to \(1 \frac{1}{20}\). We can convert \(1 \frac{1}{20}\) to an improper fraction:
\[ 1 \frac{1}{20} = \frac{21}{20} \]
Therefore, we have:
\[ \frac{3x}{5y} = \frac{21}{20} \]

5. **Cross Multiply to Solve for \(x\) and \(y\)**:
Cross multiplying gives:
\[ 3x \cdot 20 = 21 \cdot 5y \]
Simplifying this, we get:
\[ 60x = 105y \]

6. **Rearranging the Equation**:
We can rearrange this equation to express \(x\) in terms of \(y\):
\[ \frac{x}{y} = \frac{105}{60} = \frac{7}{4} \]

7. **Conclusion**:
The original fraction \(\frac{x}{y}\) can be expressed as:
\[ \frac{x}{y} = \frac{7}{4} \]
Therefore, the original fraction is \(\frac{7}{4}\).

### Final Answer:
The original fraction is \(\frac{7}{4}\).