Question

A fraction become 9./11 if 2 is added to both the numerator and denominator. if 3 is added to both the numerator and the denominator it becomes 5/6.find the fraction​

Answer 1

Given,

• If 2 is added to both the numerator and denominator then the fraction became 9/11 .
• If 3 is added to both the numerator and the denominator then it becomes 5/6 .

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be x

And , Suppose the denominator be y

According to First Conditions :-

• If 2 is added to both numerator and denominator, the fraction becomes 9/11.

$\implies \sf{\dfrac{x + 2}{y + 2} = \dfrac{9}{11}}$

$\implies \sf{11(x + 2) = 9 (y + 2)}$

$\implies \sf{11x + 22 = 9y +18}$

$\implies \sf{11x = 9y + 18 - 22}$

$\implies \boxed{\sf{ x = \dfrac{9y - 4 }{11}}}$

According to Second Condition :-

• If 3 is added to both numerator and denominator, the fraction becomes 5/6.

$\implies \sf{\dfrac{x + 3}{y + 3} = \dfrac{5}{6}}$

$\implies \sf{6(x + 3) = 5(y + 3)}$

$\implies \sf{6x + 18 = 5y + 15}$

$\implies \sf{6x - 5y = 15 - 18}$

$\implies \sf{6 ( \dfrac{9y -4 }{11} ) - 5y = - 3}$

(From First Condition the value of x Put )

$\implies \sf{\dfrac{54y - 24 }{11} - 5y = -3}$

$\implies \sf{\dfrac{54y - 24 - 55y }{11} = -3}$

$\implies \sf{\dfrac{-y - 24}{11} = -3}$

$\implies \sf{ - y - 24 = -33}$

$\implies \sf{ - y = - 33 + 24}$

$\implies \boxed{\sf{ y = 9}}$

Now Put value of y in First Condition :-

$\implies \sf{x = \dfrac{9y - 4}{11}}$

$\implies \sf{ x = \dfrac{9(9) - 4}{11}}$

$\implies \sf{x = \dfrac{81 - 4}{11}}$

$\implies \sf{x = \dfrac{77}{11}}$

$\implies \boxed{\sf{x = 7}}$

Therefore ,

$\boxed{\sf{\blue{The \ Fraction = \dfrac{7}{9}}}}$

$\rule{200}2$

Answer 2

Answer:

The fraction is 7/9

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