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 fraction?

Answer 1

let $\frac{a}{b}$ be the fraction

then

$\frac{a+1}{b-1}=1$

&

$\frac{a}{b+1}=\frac{1}{2}$

$2a-b=1$

$a+1=b-l$

$a=1+2$

$a=3$

$\therefore b=5$

$\therefore \frac{3}{5}$

is the fraction