What term should be subtracted each of the ratio `a : b` to make the ratio `m : n` ?

Explanation

Let x should be subtracted from each term.
As per question, `(a - x) : (b -x) = m : n`
or, `(a-x)/(b-x) = m/n`
or, `mb - mx = na - nx`
or, `nx - mx = na - mb`
or, `x ( n -m) = na - mb`
or, ` x = (na - mb)/(n -m) = (bm - an)/(m-n)`
Hence `(bm -an)/(m-n) ` should be subtracted.