Question

A certain fraction becomes $\frac{1}{2}$ when its numerator is increased by unity and $\frac{1}{3}$ when its denominator is increased by unity what is the fraction

• A. $\frac{5}{9}$
• B. $\frac{7}{16}$
• C. $\frac{3}{8}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{3}{8}$

Given, if the numerator is increased by $1$, then fraction $=\frac{x+1}{y}=\frac{1}{2}$
$=>2x+2=y$
$=>2x-y=-2$ --- (1)
Also, if the denominator are each increased by $1$, then fraction $=\frac{x}{y+1}=\frac{1}{3}$
$=>3x=y+1$
$=>3x-y=1$ --- (2)

Subtracting equation $\left(1\right)$
from $\left(2\right)$, we get $x=3$

Substituting $x=3$ in the
equation $\left(1\right)$, we get $2\left(3\right)-y=-2=>y=8$

Hence, the fraction is $\frac{3}{8}$