Two numbers are in the ratio 3:5.
Let the first number be 3x and the second number be 5x, where x is a common multiplier.
After the changes:
- First number becomes 3x−3
- Second number becomes 5x+3
- New ratio is 1:3
This gives us:
5x+33x−3=31
3(3x−3)=1(5x+3)
9x−9=5x+3
9x−5x=3+9
4x=12
x=3
The actual numbers are:
First number =3x=3×3=9
Second number =5x=5×3=15
Sum =9+15=24
Therefore, the sum of the numbers is 24.