The sum of the numerator and denominator of afraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3. There are in the ratio 2:3 determine the fraction

Let the fraction be x/y where x=numerator and y=denominator.

Clearly there are two cases:

**Case 1**

According to question,

x+y=2x+4

=>** **-x+y=4 =>** x-y=-4---1) **

**Case 2**

According to question,

x+3/y+3=2/3

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

=>3x+9=2y+6

=>**3x-2y=-3---2)**

By elimination method,we get:

**3x-3y=-12----3)****3x-2y=-3------4)**

By subtracting 3) and 4),we get:

-3y+2y=-12+3

=> -y=-9

So, y=9

On substituting y=9 in 4),we get:

3x-18=-3

=> 3x=15

So, x=5

Here, x=5 and y=9.

__Therefore,the fraction is:__

x/y = 5/9

**Answer: ** 5/9

Hope it helps you a lot

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