• # question_answer If 1 1s subtracted from the numerator of a fraction it becomes (1/3) and if 5 is added to the denominator the fraction becomes (1/4). Which fraction shall result, if 1 is subtracted from the numerator and 5 is added to the denominator? A)  $\frac{5}{12}$                                  B)  $\frac{7}{23}$                      C)  $\frac{1}{8}$                                    D)  $\frac{2}{3}$

Correct Answer: C

Solution :

Let the numerator and denominator of a fraction are x and y, respectively, According to question $\frac{x-1}{y}=\frac{1}{3}\Rightarrow 3x=3=y\Rightarrow 3x-y=3$  ?.(i) and    $\frac{x}{y+5}=\frac{1}{4}\Rightarrow 4x-y=5$     ?..(ii) On solving eqs. (i) and (ii), we get $x=2$ and $y=3$ $\therefore$  Required fraction             $=\frac{x-1}{y+5}=\frac{2-1}{3+5}=\frac{1}{8}$

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