The two numbers are in the ratio 3:5.
Let the first number =3x and the second number =5x for some common multiplier x.
When 9 is subtracted from each number, the new ratio becomes 12:23.
5x−93x−9=2312
23(3x−9)=12(5x−9)
69x−207=60x−108
69x−60x=207−108
9x=99
x=11
The two numbers are:
First number =3x=3×11=33
Second number =5x=5×11=55
Therefore, the greater number is 55.