Question

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

Answer 1

$\large \underline{ \underline{ \bold{ \: Answer : \: \: \: }}}$

$\to$ Original fraction = 7/12

$\large \underline{ \underline{ \bold{ \: Explaination : \: \: \: }}}$

Let ,

Numerator = x

Denominator = 2x - 2 ----- eq (i)

If 3 is added to the nunumerator and denominator

Numerator= x + 3

Denominator= 2x - 2 + 3 = 2x + 1

A.T.Q ,

$\to \frac{x + 3}{2x + 1} = \frac{2}{3} \\ \\ \to</p><p>3(x+3)=2(2x+1) \\ \\ \to</p><p>3x+9=4x+2 \\ \\ \to</p><p>3x-4x=2-9 \\ \\ \to</p><p>x=7$

Put the value of x = 7 in eq (i)

$\to$ Denominator = 2(7) - 2

$\to$ Denominator = 14 - 2

$\to$ Denominator = 12

Therefore , the original fraction is 7/12

Answer 2

Answer:

the fraction is 7/12. Let the numerator be X then the denominator=2x-2. then according to the question if 3 is added to both the numerator and denominator. the numerator and denominator become=X+3/2x-2+3=X+3/2x+1

now again according to the question ,X+3/2x+1=2/3, by cross multiplication the value of X is 7. and then by putting the value of X to the numerator and denominator the fraction we get=7/12