If the numerator of a fraction is increased by 600 % and the denominator is increased by 200% , the resulting fraction is `2(4)/(5)` . What was the original fraction ?

Options

A. `(4)/(7)`
B. `(13)/(12)`
C. `(11)/(12)`
D. `(6)/(5)`

Explanation

To solve the problem step by step, let's denote the original fraction as \( \frac{x}{y} \).

### Step 1: Understanding the changes to the fraction
- The numerator \( x \) is increased by 600%.
- The denominator \( y \) is increased by 200%.

### Step 2: Expressing the changes mathematically
- Increasing the numerator \( x \) by 600% means that the new numerator becomes:
\[ x + 600\% \text{ of } x = x + 6x = 7x \]
- Increasing the denominator \( y \) by 200% means that the new denominator becomes:
\[ y + 200\% \text{ of } y = y + 2y = 3y \]

### Step 3: Setting up the equation for the new fraction
The resulting fraction after these changes is given as \( 2 \frac{4}{5} \). We can convert this mixed number into an improper fraction:
\[ 2 \frac{4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]
Thus, we have:
\[ \frac{7x}{3y} = \frac{14}{5} \]

### Step 4: Cross-multiplying to eliminate the fraction
Cross-multiplying gives us:
\[ 7x \cdot 5 = 14 \cdot 3y \]
This simplifies to:
\[ 35x = 42y \]

### Step 5: Solving for the original fraction \( \frac{x}{y} \)
Rearranging the equation:
\[ \frac{x}{y} = \frac{42}{35} \]
This can be simplified by dividing both the numerator and denominator by 7:
\[ \frac{x}{y} = \frac{6}{5} \]

### Conclusion
The original fraction is:
\[ \frac{6}{5} \]