Question

the denominator of a fraction is 4 more than twice its numerator if 6 is subtracted from both the numerator and the denominator the denominator becomes 12 times the numerator find the fraction​

Answer 1

$\Large{ \mathfrak{ \underline{ Question : }}} \\ \\ \sf The \: denominator \: of \: fraction \: is \: 4 \\ \sf more \: than \: twice. \: The \: numerator \\ \sf and \: denominator \: are \: decreased \: by \\ \sf 6 \: then \: the \: denominator \: becomes \\ \sf 12 \: times \: the \: numerator. \: Find \\ \sf the \: fraction. \\ \\ \Large{ \mathfrak{ \underline{ Answer : }}} \\ \\ \overline { \underline{ \: \: \boxed{\sf Fraction = \frac{7}{18} } \: \: }} \\ \\ \Large{ \mathfrak{ \underline{ Solution : }}} \\ \\ \textsf{Let the Numerator be x.} \\ \therefore \textsf{Denominator = 2x + 4} \\ \\ \sf \underline{ATQ, \: We \: have} \\ \qquad \rm \implies 12(x - 6) = 2x + 4 - 6 \\ \qquad \rm \implies 12x - 72 = 2x - 2 \\ \qquad \rm \implies 12x - 2x = 72 - 2 \\ \qquad \rm \implies 10x = 70 \\ \qquad \rm \implies x = \frac{7 \cancel0}{1 \cancel0} \\ \qquad \rm \implies x = 7 \\ \\ \boxed{ \mathfrak{ Numerator = \boxed{7}}} \\ \boxed{ \mathfrak{ Denominator = 2 \times 7 + 4 = \boxed{18}}} \\ \\ \sf Fraction \\ \qquad \sf = \frac{Numerator}{Denominator} \\ \sf \qquad = \large \boxed{ \sf\frac{7}{18}}$