# 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