• # question_answer The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes $\frac{1}{5}$. Then the original number was ____. A)  $\frac{7}{11}$                     B)  $\frac{3}{5}$           C)  $\frac{5}{8}$                       D)         $\frac{4}{7}$

Let the number be $\frac{x}{y}$ According to the question,                      $y=x+3$ $\Rightarrow$  $x=y-3$                .....(1) Also, $\frac{x-3}{y+2}=\frac{1}{5}$  $\Rightarrow$  $5x-15=y+2$ $\Rightarrow$            $5x=y+17$                ??(2) Solving (1) and (2), we get $x=5$and $y=8~$ $\therefore$  Required number $=\frac{x}{y}=\frac{5}{8}$