Question

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

Answer 1

The first statement leads to,

$\frac{n+1}{d-1}=1$

or

$n+1=d-1n-d=-\mathrm{2...}\left(i\right)$

The second statement leads to,

$\frac{n}{d+1}=\frac{1}{2}$

which gives,

$2n=d+\mathrm{1..}\left(ii\right)$

Solving the above two equations simultaneously,

$n=3,d=5$

Hence the fraction is $\frac{3}{5}$