Question

Question number 16 b$$\begin{gathered} Thesumofnumeratoranddenominatorofafractionisthreelessthantwicethedenominator.Ifeachofnumeratoranddenoeminatorisdecreasedbyoneofthefractionbecomes\frac{1}{2} \\ Findthefraction. \end{gathered}$$

Answer 1

Dear student,

$$\begin{gathered} LettheNumeratoroffractionbex \\ andDenominatoroffractionbey \\ Acc.toquestion, \\ x+y+3=2y \\ \Rightarrow x+y-2y=-3 \\ \Rightarrow x-y=-3--\left(1\right) \\ Also,\frac{x-1}{y-1}=\frac{1}{2} \\ \Rightarrow 2\left(x-1\right)=y-1 \\ \Rightarrow 2x-2=y-1 \\ \Rightarrow 2x-y=-1+2 \\ \Rightarrow 2x-y=1--\left(2\right) \\ From\left(1\right)and\left(2\right) \\ x-y=-3 \\ 2x-y=1 \\ \underline{-+-} \\ -x=-4 \\ \Rightarrow \boxed{x=4} \\ Putx=4in\left(1\right) \\ \Rightarrow 4-y=-3 \\ \Rightarrow -y=-3-4 \\ \Rightarrow -y=-7 \\ \Rightarrow \boxed{y=7} \\ Thustherequiredfractionis\frac{x}{y}=\frac{4}{7} \end{gathered}$$

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