Question

in a fraction twice the numerator is 2 more than the denominator if 3 is added to the numerator and to the denominator the new fraction is 2/3 find the original fraction

Answer 1

Let the numerator be x

Denominator = 2x − 2

Therefore the fraction = x/2x − 2

Given when 3 is added to both the numerator and denominator, the fraction becomes 2/3.

Hence (x + 3)/(2x  − 2 + 3) = 2/3  

⇒ (x + 3)/(2x + 1) = 2/3  

⇒ 3x + 9 = 4x + 2  

⇒ x = 7

Therefore the fraction is 7/12.

Answer 2

Correct Question :

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3 . Find the original fraction.

Given :

In a fraction, twice the numerator is 2 more than the denominator.

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

To find :

The original fraction.

Solution :

Let the numerator be x and the denominator be y .

According to the 1st condition :-

In a fraction, twice the numerator is 2 more than the denominator.

$\implies\sf{2x=y+2}$

$\implies\sf{y=2x-2........eq(1)}$

According to 2nd condition :-

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

$\implies\sf{\frac{x+3}{y+3}=\frac{2}{3}}$

$\implies\sf{3x+9=2y+6}$

✪ Now put the value of y=2x-2 from eq (1)✪

$\implies\sf{3x+9=2(2x-2)+6}$

$\implies\sf{3x+9=4x-4+6}$

$\implies\sf{3x-4x=-9+2}$

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

$\implies\sf{x=7}$

✪ Now put x = 7 in eq(1) ✪

$\implies\sf{y=2x-2}$

$\implies\sf{y=2\times\:7-2}$

$\implies\sf{y=14-2}$

$\implies\sf{y=12}$

★ Numerator = 7

★ Denominator = 12

${\boxed{\bold{Fraction=\dfrac{Numerator}{Denominator}}}}$

Therefore,

${\boxed{\purple{\bold{Original\: fraction=\dfrac{x}{y}=\dfrac{7}{12}}}}}</p><p>$