Question

If we add 1 to numerator and subtract 1 from the denominator a fraction reduces to 1. It become 1/2 if we only add 1 to the denominator. what is fraction?​

Answer 1

$\huge\mathcal\color{red} AnSwEr::$

➣

$\: \rightarrow\: \bold{Let \: the \: numerator \: of \: a \: fraction \: be \: x.} \:$

$\:\rightarrow\: \bold{And\: the\: denominator\: of\: a\: fraction\: be \: y.} \:$

$\implies \Large \bold{Original \: fraction} = \bold{ \frac{x}{y} }$

$\rightarrow \: \Large\mathtt{ \frac{x + 1}{y - 1} } = 1$

$\rightarrow \: \large\mathtt{x + 1 = y - 1} \\ \: \: \: \: \: \: \mathtt{x - y = - 2 \: \: \: eq(1)}$

$\rightarrow \: \Large \mathtt{ \frac{x}{y + 1} = \frac{1}{2}}$

$\rightarrow \: \mathtt{2x = y + 1} \\ \: \: \: \: \: \: \mathtt{2x - y = 1 \: \: eq(2)}$

$\rightarrow \: \mathtt{x - y = - 2} \\ \: \: \: \: \: \: \mathtt{2x - y = 1}$

$\: \large\bold{Now \: change\: the\: sign \: of \: 2x-y= 1} \:$

$\rightarrow \: \mathtt{x - y = - 2} \\ \: \: \: \mathtt{ \frac{ - 2x + y = - 1}{ \cancel {- }x = \cancel{ - }3} } \\ \: \: \: \: \: \: \: \: \: \: \large\fbox\mathtt{ x = 3}$

$\: \bold{Put\: x=3\: in\: eq. (1)} \:$

$\rightarrow \: \mathtt{x - y = - 2} \\ \: \: = \mathtt{3 - y = - 2} \\ \: \: \mathtt{ - y = - 2 - 3} \\ \: \: \: \mathtt{ \cancel{ - }y = \cancel{ - }5} \\ \: \: \: \: \: \: \fbox \mathtt {y = 5}$

$\: \Large\fbox\mathtt{Fraction = \frac{x}{y} = \fbox{ \frac{3}{5} }}$

${\huge{\purple{\mathtt{BeBrainly...!}}}}$