Math, asked by gfsf, 1 year ago

in a certain fraction the denominator is 4 less than numerator if 3 is added to both the numerator amd deominator the resulting fraction is 9/7 find the original number

Answers

Answered by Anonymous
5

Answer:

Let the Numerator be x and Denominator be x - 4

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\underline{\boldsymbol{According\: to \:the\: Question\:now :}}

:\implies\sf \dfrac{Numerator + 3}{Denominator + 3} = \dfrac{9}{7} \\  \\  \\

:\implies\sf \dfrac{x + 3}{x - 4 + 3} = \dfrac{9}{7} \\  \\  \\

:\implies\sf \dfrac{x + 3}{x - 1} = \dfrac{9}{7} \\  \\  \\

:\implies\sf (x + 3)7 = 9(x - 1) \\  \\  \\

:\implies\sf 7x + 21 = 9x - 9 \\  \\  \\

:\implies\sf 21  + 9 = 9x - 7x \\  \\  \\

:\implies\sf 30 = 2x \\  \\  \\

:\implies\sf x =  \dfrac{30}{2} \\  \\  \\

:\implies \underline{ \boxed{\textsf{ \textbf{x = 15}}}} \\  \\

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\boxed{\bf{\mid{\overline{\underline{\bigstar\: Therefore :}}}}\mid}\\ \\

\bullet\:\:\textsf{Numerator = x = \textbf{15}}

\bullet\:\:\textsf{Denominator = x - 4 = 15 - 4  = \textbf{11}}

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\therefore\:\underline{\textsf{Required \: fraction \: is \: \textbf{$ {} {\text{15}}\!/{}_{\text{11}}$}}}. \\

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