Question

A fraction becomes 4/5 if 1 is added to numerator and becomes 1/2 if 5 is substracted from numerator and denominator . Find the fraction

Answer 1

$\large \mathfrak \red{Given:-}$

$\tt{A \: fraction \: become s \: 4/5} \\ \tt{ if \: 1 \: i s \: added \: to \: numerator.}$

$\: \: \: \: \: \: \tt{Let \: numerator \: be \: x \: and } \\ \: \: \: \: \: \: \tt{denominator \: be \: y.}$

$\\ \: \: \: \: \: \: \tt{ \frac{4}{5} = \frac{x + 1}{y} }$

$\: \: \: \: \: \: \tt{4y = 5x + 5.}$

$\: \: \: \: \: \: \tt{5x - 4y = - 5. - - - (1)}$

$\tt{and \: becomes \: 1/2 \: if \: 5 \: is } \\ \tt{substracted \: from} \\ \tt{numerator \: and \: denominator.}$

$\\ \: \: \: \: \: \: \tt{ \frac{1}{2} = \frac{x - 5}{y - 5} }$

$\: \: \: \: \: \: \tt{y - 5 = 2x - 10.}$

$\: \: \: \: \: \: \tt{2x - y = 5. - - - (2)}$

$\tt{Find \: the \: fraction.}$

$\tt{From \: equation} \\ \: \: \: \: \: \tt{ (1 ) \times \: 2 \: and \: 2 \times 5 ,we \: get}$

$\\ \: \: \: \: \: \: \tt{3y = 15.}$

$\: \: \: \: \: \: \tt{y = 5.}$

$\tt{Putting \: the \: value \: of \: y= 5 } \\ \tt{in \: equation \: (2)}$

$\: \: \: \: \: \: \tt{2x - y= 5.}$

$\: \: \: \: \: \: \tt{2x - 5 = 5.}$

$\: \: \: \: \: \: \tt{2x = 10.}$

$\: \: \: \: \: \: \tt{x = 5.}$

$\tt{Therefore, the \: numerator \: be } \\ \: \: \: \: \: \: \: \: \: \: \: \: \tt{5 \: and \: denominator \: be \: 5.}$