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