If the numerator of a fraction is increased by 200% and the denominator is increased by 200%, then resultant fraction is `2 4/5`. What is the original fraction?

Options

A. `4//7`
B. `13//12`
C. `11//12`
D. None of these

Answer

To solve the problem, we need to find the original fraction given that both the numerator and denominator are increased by 200%, resulting in a new fraction of \(2 \frac{4}{5}\).

### Step-by-step Solution:

1. **Understand the Problem**:
- Let the original fraction be \(\frac{X}{Y}\), where \(X\) is the numerator and \(Y\) is the denominator.
- When the numerator \(X\) is increased by 200%, it becomes \(X + 2X = 3X\).
- When the denominator \(Y\) is increased by 200%, it becomes \(Y + 2Y = 3Y\).

2. **Set Up the Equation**:
- The new fraction after the increases is given as \(2 \frac{4}{5}\), which can be converted to an improper fraction:
\[ 2 \frac{4}{5} = \frac{14}{5} \]
- Therefore, we can set up the equation:
\[ \frac{3X}{3Y} = \frac{14}{5} \]

3. **Simplify the Equation**:
- The \(3\) in the numerator and denominator cancels out:
\[ \frac{X}{Y} = \frac{14}{5} \]

4. **Express the Original Fraction**:
- From the equation \(\frac{X}{Y} = \frac{14}{5}\), we can express \(X\) in terms of \(Y\):
\[ X = \frac{14}{5}Y \]
- Thus, the original fraction can be expressed as:
\[ \frac{X}{Y} = \frac{\frac{14}{5}Y}{Y} = \frac{14}{5} \]

5. **Conclusion**:
- The original fraction is \(\frac{14}{5}\).