Question

If we add 1 to the numerator and subtract 1 from the denominator a fraction becomes 1. It also becomes $\frac{1}{2}$ if we only add 1 to the denominator what is the numerator of the fraction?

• A. 2
• B. 4
• C. 5
• D. 3

Answer 1

The correct option is D 3

Suppose the fraction is $\frac{x}{y}$
If 1 is added to the numerator and 1 is subtracted to the denominator the fraction becomes 1
$\frac{x+1}{y-1}=1$
$x+1=y-1$
$x-y=-2$ Equation (1)
If 1 is added to the denominator the fraction becomes half
$\frac{x}{y+1}=\frac{1}{2}$
$2x=y+1$
$2x-y=1$ Equation (2)
On subtracting Equation 1 from 2 we get
$2x-y-x+y=1+2$
$x=3$
Substituting the value of x in equation 1 we get,
$3-y=-2$
$y=5$
$\frac{x}{y}=\frac{3}{5}$
Numerator is $3$.