Question

The denominator of a fraction is 2 more than the numerator. If 1 is added to each of the numerator and the denominator of the fraction, then the fraction becomes 3/4.​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

The denominator of a fraction is 2 more than the numerator. If 1 is added to each of the numerator and the denominator of the fraction, then the fraction becomes 3/4.

$\bf \underline{\underline{\maltese\: To \: find }}$

$\sf \implies Original \: fraction = \: ?$

$\bf \underline{\underline{\maltese\: Solution }}$

$\sf Let, the \: numerator \: be \: x$

$\bf \underline{ Then},$

$\sf The \: denominator \: will \: be \: x + 2$

$\bf \underline{ According \: to \: question},$

$\sf Equation \implies\red { \bf{\cfrac{x + 1}{x + 2 + 1} = \cfrac{3}{4} }}$

$\sf \underline{Now, we \: will \: solve \: the \: above \: equation. }$

$\sf \implies{\cfrac{x + 1}{x +3} = \cfrac{3}{4} }$

$\sf \implies4(x + 1) = 3(x + 3)$

$\sf \implies4x + 4= 3x + 9$

$\sf \implies4x - 3x = 9 - 4$

$\sf \implies \bf x = 5$

$\sf Now, the \: original \: fraction \: will \: be :$

$\sf \implies \sf{\cfrac{x}{x + 2} } = \sf{\cfrac{5}{5 + 2} } = \bf \dfrac{5}{9}$

$\bf \underline{Therefore},$

$\underline{ \boxed{ \red{ \bf The \: original \: fraction \: is \:\dfrac{5}{9} }}}$