Question

If the numerator of a fraction is increased by 2 and denominator is decreased by 1, it becomes $\frac{2}{3}$. If the numerator is increased by 1 and denominator is increased by 2, it becomes $\frac{1}{3}$. Find the fraction.

• A. $\frac{2}{7}$
• B. $\frac{1}{5}$
• C. $\frac{7}{9}$
• D. $\frac{5}{3}$

Answer 1

The correct option is A $\frac{2}{7}$

Let the fraction be $\frac{x}{y}$
Given, if the numerator of a fraction is increased by $2$ and denominator is decreased by $1$, then fraction $=\frac{x+2}{y-1}=\frac{2}{3}$
$=>3x+6=2y-2$
$=>3x-2y=-8$ --- (1)
Also, if the numerator is increased by $1$ and denominator is increased by $2$ then fraction $=\frac{x+1}{y+2}=\frac{1}{3}$
$=>3x+3=y+2$
$=>3x-y=-1$ --- (2)
Subtracting equation $\left(1\right)$ from $\left(2\right)$, we get $y=7$

Substituting $y=7$ in the equation $\left(2\right)$, we get $3x-7=-1=>x=2$ Hence, the fraction is $\frac{2}{7}$