Question

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 1

Answer:

Hey mate here is the answer..

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Step-by-step explanation:

Ur answer is in the attachment below....

Answer 2

$\large{\underline{\underline{\tt{\red{Answer-}}}}}$

$\large{\boxed{\rm{\blue{Fraction\:=\:\dfrac{7}{9}}}}}$

$\large{\underline{\underline{\tt{\red{Explanation-}}}}}$

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 = $\tt{\dfrac{x}{y}}$

$\huge{\rightarrow}$ $\large{\boxed{\rm{\blue{Fraction\:=\:\dfrac{7}{9}}}}}$