Finding an unknown fraction

A fraction has numerator \(n\) and denominator \(d\). If \(2\) is subtracted from the numerator and \(3\) is added to the denominator, the fraction becomes \(\frac{1}{3}\). If \(4\) is added to the numerator and \(3\) is subtracted from the denominator, the fraction becomes \(1\).

1. Form two equations in \(n\) and \(d\).
2. Solve the equations obtained in (a) to find \(n\) and \(d\).
3. Hence, state the original fraction in its simplest form.