Question

The numerator of a fraction is 2 less than its denominator . If 1 is added to both its numerator and denominator it becomes 2 \ 3 . Find the fraction

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{denominator}\mathrm{of}\mathrm{fraction}\mathrm{be}\mathrm{x}. \\ \mathrm{Numerator}=\mathrm{x}-2 \\ \mathrm{Fraction}=\frac{\mathrm{x}-2}{\mathrm{x}} \\ \mathrm{When}1\mathrm{is}\mathrm{added}\mathrm{to}\mathrm{both}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{then} \\ \mathrm{Denominator}=\mathrm{x}+1 \\ \mathrm{Numerator}=\mathrm{x}-2+1=\mathrm{x}-1 \\ \mathrm{New}\mathrm{fraction}=\frac{2}{3} \\ \frac{\mathrm{x}-1}{\mathrm{x}+1}=\frac{2}{3} \\ 3\mathrm{x}-3=2\mathrm{x}+2 \\ \mathrm{x}=5 \\ \mathrm{Fraction}=\frac{5-2}{5} \\ =\frac{3}{5}\mathrm{ANS}... \end{gathered}$$

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