The numerator of a certain fraction is to its denominator as 2 to 3; if 5 be added to the numerator the ratio will be as 3 to 2; what is the fraction?

N = numerator

D = denominator

N:D = = > 2:3

2:3, 4:6, 6:9 ... And so on ...

The pattern here is that the numerator increases by 2 and the denominator by 3. Easy right?

Now 5 is added to the "n".

Now it is N:D = = > 3:2

3:2, 6:4, 9:6 ... And so on ...

The pattern here is inverted then the 2:3 one.

If I'm right then which one (you might have to continue the process/pattern) then one of them will increase by 5.

3 = > 2 = + 1 (2+1=3)

6 = > 4 = + 2 (4+2=6)

9 = > 6 = + 3 (6+3=9)

12 = > 8 = + 4 (8+4=12)

15 = > 10 = + 5 (10+5=15)

18 = > 12 = + 6 (12+6=18)

Q. Which one is + 5?

A. 15:10

That is what "I" think it is.

Now, the question is,

Does it work? Does it fit the above description?

Q. Does it even work? Does it fit the above description?