A fraction becomes 1/3 when 2 …

Let the fraction be {tex}\frac{x}{y}{/tex}
According to the question, the fraction becomes {tex}\frac{1}{3}{/tex} when 2 is subtracted from the numerator.
{tex}\therefore{/tex} {tex}\frac{x-2}{y}{/tex} = {tex}\frac{1}{3}{/tex} 
By cross multiplying, we get
{tex}\Rightarrow 3x -6 = y{/tex}...(i)
According to the question, the fraction becomes {tex}\frac{1}{2}{/tex} when 1 is subtracted from the denominator.
{tex}\therefore{/tex}{tex}\frac{x}{y-1}{/tex} = {tex}\frac{1}{2}{/tex} 
By cross multiplying, we get
{tex}\Rightarrow 2x = y-1{/tex}....(ii)
Substituting (i) in (ii), we get
{tex} \Rightarrow 2x = 3x-6 -1 \\\Rightarrow x =7{/tex}
Substituting x in (i), we get
{tex}\Rightarrow 21-6 = y \\\Rightarrow y=15{/tex}
{tex}\therefore x = 7, y = 15{/tex}
{tex}\therefore{/tex} Required fraction if {tex}\frac{7}{15}.{/tex}