Question

the numerator of a fraction is 5 less then the denominator . if 9 is added to both numerator and denominator than it becomes 2/3 . find the number

Answer 1

Let the denominator be x and numerator be 5 less than denominator i.e. ( x - 5 ) ,

Then, original fraction = Numerator / Denominator

Original fraction = ( x - 5 ) / x

Given, when 9 is added to both numerator and denominator then it becomes 2 / 3

According to the question,

⇒ ( numerator + 9 ) ÷ ( denominator + 9 ) = 2 ÷ 3

⇒ ( x - 5 + 9 ) ÷ ( x + 9 ) = 2 ÷ 3

⇒ ( x + 4 ) ÷ ( x + 9 ) = 2 ÷ 3

⇒ 3( x + 4 ) = 2( x + 9 )

⇒ 3x + 12 = 2x + 18

⇒ 3x - 2x = 18 - 12

⇒ x = 6

Hence,

Original fraction is ( x - 5 ) / x = ( 6 - 5 ) / 6 = 1 / 6

$\boxed{ \bold{ \underline{ Original\;\;\ Fraction} = \frac{1}{6}}}$

Answer 2

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$Let \: the \: denominator \: be \: x \\ Let \: the \: numerator \: be \: (x - 5) \\ So, \: The \: fraction \: becomes \: \frac{x - 5}{x} \\ \\ Now ,\: Acc.to \: statement : \\ \\ = > \frac{(x - 5) + 9}{x + 9} = \frac{2}{3} \\ \\ = > \frac{x + 4}{x + 9} = \frac{2}{3} \\ \\ = > 3(x +4) = 2(x + 9) \\ \\ = > 3x + 12 = 2x + 18 \\ \\ = > x = 18 -12 \\ \\ = > x = 6 \\ \\ So, \: The \: denominator \: is \: 6 \\ \\ and \: The \:Numerator \: is \: 1 \\ \\ Fraction \: becomes = 1/6$
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