Question :A fraction becomes 9/11, if 2 is added to both the numerator

1.	Question :A fraction becomes 9/11, if 2 is added to both the numerator & denominator. If 3 is added to both the numerator & denominator it becomes 5/6. Find the fraction.
Answer» $\large{\underline{\underline{\tt{\red{Answer-}}}}}$ $\large{\boxed{\rm{\blue{Fraction\:=\:\dfrac{7}{9}}}}}$ $\large{\underline{\underline{\tt{\red{Explanation-}}}}}$ Let the numerator and denominator be X and y respectively. $\rightarrow$ Fraction = $\tt{\dfrac{x}{y}}$ $\bold{\pink{\rm{According\:to\:the\:question-}}}$ If 2 is added to both the numerator & denominator, the fraction BECOMES $\tt{\dfrac{9}{11}}$ $\therefore$ $\tt{\dfrac{x+2}{y+2}\:=\:\dfrac{9}{11}}$ $\rightarrow$ $\tt{11(x+2)\:=\:9(y+2)}$ $\rightarrow$ 11x + 22 = 9y + 18 $\rightarrow$ 11x + 22 - 9y - 18 = 0 $\rightarrow$ 11x - 9y = -4 $\rightarrow$ x = $\tt{\dfrac{9y-4}{11}}$ __________(1) $\rule{200}2$ If 3 is added to both the numerator & denominator it becomes 5/6. $\therefore$ $\tt{\dfrac{x+3}{y+3}\:=\:\dfrac{5}{6}}$ $\rightarrow$ 6x + 18 = 5y + 15 Putting the value of x, $\rightarrow$ 54 - 24 = 55y - 33 $\rightarrow$ $\tt{\cancel{-}\:y\:=\:\cancel{-}\:9}$ $\large{\boxed{\tt{\pink{y\:=\:9}}}}$ ★ Now, put the value of y in (1), $\rightarrow$ x = $\tt{\dfrac{81-4}{11}}$ $\rightarrow$ x = $\tt{\cancel{\dfrac{77}{11}}}$ $\large{\boxed{\tt{\purple{x\:=\:7}}}}$ $\rule{200}2$ ★ Fraction = $\tt{\dfrac{x}{y}}$ $\huge{\rightarrow}$ $\large{\boxed{\rm{\blue{Fraction\:=\:\dfrac{7}{9}}}}}$