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 2/ 3 find the original fraction

Answer 1

Here is the solution,

Let denominator be x and numerator be y,

Now according to the question,
2y = x +2,
=> x = 2y-2,

Now the fraction is,
(y)/(2y-2)

Again according to the question,

(y+3)/(2y+1) = 2/3, Cross multiply,
=> 3y + 9 = 4y + 2
=> y = numerator = 7, and denominator = 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,

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