If 1 is added to the denominator of a fraction it becomes `(1)/(2)` . If 1 is added to the numerator, it becomes 1. The product of numerator and denominator of the fraction is

Options

A. 6
B. 10
C. 12
D. 14

Answer

To solve the problem step by step, we will denote the fraction as \( \frac{x}{y} \), where \( x \) is the numerator and \( y \) is the denominator.

### Step 1: Set up the equations based on the conditions given in the problem.
1. According to the first condition, if 1 is added to the denominator, the fraction becomes \( \frac{1}{2} \):
\[ \frac{x}{y + 1} = \frac{1}{2} \]
Cross-multiplying gives us:
\[ 2x = y + 1 \quad \text{(Equation 1)} \]