Question

what number must be added to each term of the ratio 7:12 to make it 2:3

Answer 1

let the initial numbers be 7x and 12x.
Now add y in each number , the numbers are now 7x + y and 12x + y.
(7x + y)/(12x + y)=2/3
21x + 3y = 24x + 2y
y = 3x

(7+3)/(12+3)=10/15=2/3

Therefore 3 must be added to get the desired answer.