Question

A A fraction becomes to 1/3 when 1 is subtracted
from the numerator and it becomes 1/4 when 8
is added to its denominator.
Find the fraction


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Answer 1

$\bold{Let \: the \: fraction \: is \: \dfrac{x}{y}}$

According to the given condition,

A fraction becomes 1/3 when 1 is subtracted from its numerator. So,

$\begin{gathered}\dfrac{x-1}{y}=\dfrac{1}{3}\\\\3x-3=y\\\\3x-y=3\ - - - - (1)\end{gathered}$

The fraction becomes 1/4 when 8 is added to its denominator. So,

$\begin{gathered}\dfrac{x}{y+8}=\dfrac{1}{4}\\\\4x=y+8\\\\4x-y=8\ - - - - (2)\end{gathered}$

Solving equation (1) and (2) we get :

x=5

Put x = 5 in equation (1) :

$\begin{gathered}3(5)-y=3\\\\y=12\end{gathered}$

$\bold{So, the \: fraction \: is \: \dfrac{5}{12} }$