Question

the sum of numerator and denominator of a fraction is 4 more than twice the numerator if 3 is added to each of the numerator and the denominator the ratio becomes 2 ratio 3 find the fraction

Answer 1

Hey

Here is your answer,

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!