Question

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator , the new fraction is 2\3. Find the original fraction .

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numerator}=\mathrm{x} \\ \mathrm{Then}\mathrm{the}\mathrm{denominator}=2\mathrm{x}-2 \\ \mathrm{Now},\mathrm{required}\mathrm{fraction}=\frac{\mathrm{x}}{2\mathrm{x}-2} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \frac{\mathrm{x}+3}{2\mathrm{x}-2+3}=\frac{2}{3} \\ \Rightarrow \frac{\mathrm{x}+3}{2\mathrm{x}+1}=\frac{2}{3} \\ \Rightarrow 4\mathrm{x}+2=3\mathrm{x}+9 \\ \Rightarrow 4\mathrm{x}-3\mathrm{x}=9-2 \\ \Rightarrow \mathrm{x}=7 \\ \mathrm{So},\mathrm{numerator}=7 \\ \mathrm{denominator}=2\times 7-2=12 \\ \mathrm{required}\mathrm{fraction}=\frac{7}{12} \end{gathered}$$