Question

11. The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2, find the fraction. 
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Answer 1

Answer:

let the no be x

therefore denominator be x+8

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Answer 2

AnswEr :

13/21.

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

The denominator of a fraction is greater than the numerator by 8. If the numerator increased by 17 and denominator is decreased by 1, then the number obtained is 3/2.

$\bf{\red{\underline{\underline{\bf{To\:finD\::}}}}}$

The fraction.

$\bf{\purple{\underline{\underline{\bf{Explanation\::}}}}}$

Let the numerator be R

Let the denominator be R+8

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\sf{The\:fraction\:is\:\: \sf{\dfrac{R}{R+8}}}}}}$

$\sf{\underline{\bf{\dag{New\:numerator\:=\:R+17}}}}\\\\\sf{\underline{\bf{\dag{New\:denominator\:=\:R+8-1=(R+7).}}}}}$

So,

$\longrightarrow\bf{\dfrac{R+17}{R+7} =\dfrac{3}{2}} \\\\\\\\\longrightarrow\bf{2(R+17)=3(R+7)\:\:\:\;\: \underbrace{Cross-Multiplication}}\\\\\\\\\longrightarrow\bf{2R+34=3R+21}\\\\\\\\\longrightarrow\bf{2R-3R=21-34}\\\\\\\\\longrightarrow\bf{\cancel{-}R=\cancel{-}13}\\\\\\\\\longrightarrow\bf{\red{R=13}}$

Thus,

$\bf{\large{\underline{\bf{\blacksquare{The\:fraction\:is\:\dfrac{R}{R+8} =\dfrac{13}{13+8} =\dfrac{13}{21}. }}}}}$