If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is `9/(35)` . What is the orginal fractional ?

Options

A. `3/(10)`
B. `2/(15)`
C. `(3)/(14)`
D. `3/7`

Answer

To solve the problem step by step, we need to first understand the changes made to the numerator and denominator of the original fraction.

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

2. **Increase the numerator by 200%**:
- Increasing by 200% means adding 2 times the original numerator to itself.
- Therefore, the new numerator becomes:
\[ x + 200\% \text{ of } x = x + 2x = 3x \]

3. **Increase the denominator by 150%**:
- Increasing by 150% means adding 1.5 times the original denominator to itself.
- Therefore, the new denominator becomes:
\[ y + 150\% \text{ of } y = y + 1.5y = 2.5y \]

4. **Set up the equation with the resultant fraction**:
- According to the problem, the resultant fraction after these increases is \( \frac{9}{35} \). Therefore, we can set up the equation:
\[ \frac{3x}{2.5y} = \frac{9}{35} \]

5. **Cross-multiply to solve for \( x \) and \( y \)**:
- Cross-multiplying gives us:
\[ 3x \cdot 35 = 9 \cdot 2.5y \]
- Simplifying this, we get:
\[ 105x = 22.5y \]

6. **Rearranging the equation**:
- We can express \( y \) in terms of \( x \):
\[ y = \frac{105x}{22.5} \]
- Simplifying \( \frac{105}{22.5} \):
\[ y = \frac{1050}{225}x = \frac{14}{3}x \]

7. **Finding the original fraction**:
- The original fraction \( \frac{x}{y} \) can now be expressed as:
\[ \frac{x}{\frac{14}{3}x} = \frac{3}{14} \]

Thus, the original fraction is \( \frac{3}{14} \).