Question

the denominator of a rational number is greater than its numerator by 6 if the numerator is increased by 5 and denominator is decreased by 3 denominator obtained is equal to 5/4 find the rational number

Answer 1

Answer:5/11

Step-by-step explanation:

Answer 2

$\textbf{\huge\underline{\underline\red{solution} : - }} \\ \\ \tt{ \underline\red{given} : - } \\ \tt{\red{a.} }\tt{ \underline\purple{the \: denominator \: of \: a \: rational }} \\ \tt{ \underline \purple{number \: is \: greater \: than \: its }} \\ \tt{ \underline \purple{numerator \: by \: 6.}}\\\tt{\red{b.}} \tt{\underline\purple{the \: numerator \: is \: increased \: by \: 5 }} \\ \tt{ \underline \purple{and \: denominator \: is \: decreased \: by \: 3}} \\ \tt{ \underline \purple{then \: number \: obtained \: \frac{5}{4} .}} \\ \\ \tt \red{(from \: \: \: a.)} \\ \\ \tt \blue{let, \: \purple{numerator \: be \: x \:} and \:} \\ \tt \purple{ denominator \: be \: (x + 6)} \\ \\\tt{hence}\tt \purple{ \: \: = > \frac{x}{(x + 6)}} \tt{ \: \: \: \: \: \: ........(1)} \\ \\ \tt \red{from \: \: \: b.} \\ \tt {numerator \: = (x + 5) \: \: \: \: and} \\ \tt{denominator = (x + 6 - 3)}\\ \\ \tt\red{now} \\ \\ \tt \purple{ = > \frac{(x + 5)}{(x + 6 - 3)} = \frac{5}{4} } \\ \\ \tt \purple{ = > \frac{(x + 5)}{(x + 3)} = \frac{5}{4} } \\ \\ \tt \purple{ = > 4( x + 5) = 5(x + 3)} \\ \\ \tt \purple{ = >4x + 20 = 5x + 15 } \\ \\ \tt \purple{ = > 4x - 5x = 15 - 20} \\ \\ \tt \purple{ = > \cancel { -} \: x = \cancel{ -} \: 5 } \\ \\ \tt \purple{ = > x = 5} \\ \\ \tt{put \: value \: of \: \: x \: = \: 5 \: \: in \:(1) } \\ \\ \tt{so...} \\ \\ \tt{ = > \frac{x}{x + 6} = > } \tt \purple{ \: \: \frac{5}{5 + 6} = \frac{5}{11} } \\ \\ \tt\red{hence \: the \: rational \: number \: is \: \tt\purple{ \frac{5}{11} }.}$