Question

In a rational number, twice the numerator is 2 more than the denominator. If 3 is
added to each, the numerator and the denominator, the new fraction is 2/3. Find the
original number by taking numerator as x


please tell its urgent

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Answer 1

EXPLANATION.

Let the numerator of fraction be = x

Let the denominator of fraction be = 2x - 2

if 3 is added to each the numerator

and the denominator the new fraction

become = 2/3.

=> x + 3 / 2x - 2 + 3 = 2/3

=> x + 3 / 2x + 1 = 2/3

=> 3 ( x + 3 ) = 2 ( 2x + 1 )

=> 3x + 9 = 4x + 2

=> 7 = x

Therefore,

=> Numerator = 7

=> Denominator = 2x - 2 = 2(7) - 2 = 12

Fraction become = 7/12.

Answer 2

Answer:

Let the Numerator be x and Denominator be (2x - 2) of the Fraction.

If 3 is added to each, the numerator and the denominator, the new fraction is 2/3

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{Numerator+3}{Denominator+3}=\dfrac{2}{3}\\\\\\:\implies\sf \dfrac{x+3}{(2x - 2)+3}=\dfrac{2}{3}\\\\\\:\implies\sf \dfrac{x+3}{2x + 1}=\dfrac{2}{3}\\\\\\:\implies\sf 3(x + 3) = 2(2x + 1)\\\\\\:\implies\sf 3x + 9 = 4x + 2\\\\\\:\implies\sf 9 - 2 = 4x - 3x\\\\\\:\implies\sf x = 7$

⠀

$\dag\:\underline{\boxed{\sf Fraction=\dfrac{x}{2x - 2} = \dfrac{7}{2(7) - 2} = \dfrac{7}{12} }}$