If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 250%, the resultant fraction is 3/14. What is the original fraction ?

Options

A. 1/6
B. 1/4
C. 2/3
D. 3/14

Answer

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

### Step 1: Understand the changes to the numerator and denominator
- The numerator \( x \) is increased by 200%.
- The denominator \( y \) is increased by 250%.

### Step 2: Calculate the new numerator and denominator
- An increase of 200% means the new numerator becomes:
\[ x + 200\% \text{ of } x = x + 2x = 3x \]
- An increase of 250% means the new denominator becomes:
\[ y + 250\% \text{ of } y = y + 2.5y = 3.5y \]

### Step 3: Set up the equation with the resultant fraction
According to the problem, the resultant fraction after these changes is:
\[ \frac{3x}{3.5y} = \frac{3}{14} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 3x \cdot 14 = 3.5y \cdot 3 \]
This simplifies to:
\[ 42x = 10.5y \]

### Step 5: Simplify the equation
To simplify, we can divide both sides by 10.5:
\[ \frac{42x}{10.5} = y \]
Calculating \( \frac{42}{10.5} \):
\[ \frac{42}{10.5} = 4 \]
Thus, we have:
\[ y = 4x \]

### Step 6: Find the original fraction
The original fraction can now be expressed as:
\[ \frac{x}{y} = \frac{x}{4x} = \frac{1}{4} \]

### Conclusion
The original fraction is:
\[ \frac{1}{4} \]