twice the numerator is 2 more than the denominator if 3 is added to ea

1.	twice the numerator is 2 more than the denominator if 3 is added to each the numerator and denominator then a fraction is 2 by 3 find the original number.
Answer» $\mathfrak{\large{\underline{\underline{Answer :-}}}}$ The Original Fraction is ${\bf{\dfrac{7}{12}}}$ $\mathfrak{\large{\underline{\underline{Explanation :-}}}}$ Given : TWICE the numerator = 2 more than the Denominator 3 is ADDED to numerator and Denominator = Fraction is $\tt{\dfrac{2}{3}}$ To Find : The Original fraction SOLUTION : Consider the numerator as x Denominator = 2x - 2 ★ $\green{\boxed{\tt{\red{\frac{x + 3}{(2x - 2) + 3} = \frac{2}{3}}}}}$ $\tt{\implies} \: \dfrac{x + 3}{(2x - 2) + 3} = \dfrac{2}{3}$ $\tt{\implies} \:3(x + 3) = 2(2x - 2 + 3)$ $\tt{\implies} \:3x + 9 = 4x - 4+ 6$ $\tt{\implies} \:3x + 9 = 4x + 2$ $\tt{\implies} \:4x - 3x= 9 - 2$ $\tt{\implies} \:x = 7$ $\rule{300}{1.5}$ ★ Value of 2x - 2 $\tt{\implies} \: (7 \times 2) - 2$ $\tt{\implies} \: 14 - 2$ $\tt{\implies} \: 12$ Numerator = 7 Denominator = 12 Fraction = $\boxed{\boxed{\bf{\dfrac{7}{12}}}}$ $\therefore$ The Original Fraction is ${\bf{\dfrac{7}{12}}}$ $\rule{300}{1.5}$ $\mathfrak{\large{\underline{\underline{Verification :-}}}}$ Add 3 to the numerator and Denominator to see whether the new fraction formed is $\tt{\dfrac{2}{3}}$ $\tt{\implies} \: \dfrac{7 + 3}{12 + 3} = \dfrac{2}{3}$ $\tt{\implies} \: \dfrac{10}{15} = \dfrac{2}{3}$ Reduce the Fraction $\tt{\implies} \: \dfrac{10 \div 5}{15 \div 5} = \dfrac{2}{3}$ $\tt{\implies} \: \dfrac{2}{3} = \dfrac{2}{3}$ $\therefore$ The Original Fraction is ${\bf{\dfrac{7}{12}}}$