If the numerator of a fraction is increased by 20% and the denominator is increased by 25% , the fraction obtained is `(3)/(5)` . What was the original fraction ?

Options

A. `(5)/(7)`
B. `(4)/(7)`
C. `(3)/(8)`
D. None of these

Explanation

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

### Step 1: Understand the changes in the numerator and denominator
- The numerator \( x \) is increased by 20%. Therefore, the new numerator becomes:
\[ \text{New Numerator} = x + 0.20x = 1.20x \]
- The denominator \( y \) is increased by 25%. Therefore, the new denominator becomes:
\[ \text{New Denominator} = y + 0.25y = 1.25y \]

### Step 2: Set up the equation based on the new fraction
According to the problem, the new fraction after these increases is equal to \( \frac{3}{5} \):
\[ \frac{1.20x}{1.25y} = \frac{3}{5} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 5 \cdot 1.20x = 3 \cdot 1.25y \]
This simplifies to:
\[ 6.00x = 3.75y \]

### Step 4: Simplify the equation
Dividing both sides by 1.25 to isolate \( x \) in terms of \( y \):
\[ \frac{6.00x}{3.75} = y \]
This simplifies to:
\[ \frac{6x}{3.75} = y \]
To make calculations easier, we can multiply both sides by 100 to eliminate decimals:
\[ 600x = 375y \]

### Step 5: Rearranging the equation
Rearranging gives:
\[ \frac{x}{y} = \frac{375}{600} \]

### Step 6: Simplifying the fraction
Now, simplify \( \frac{375}{600} \):
- Both 375 and 600 can be divided by 75:
\[ \frac{375 \div 75}{600 \div 75} = \frac{5}{8} \]

### Conclusion
Thus, the original fraction \( \frac{x}{y} \) is:
\[ \frac{5}{8} \]