What should be added to each term of the ratio a: b to make x: y?

Let p is to be added to each term of a: b to get the ratio x: y .

Therefore, $\frac{\mathrm{a}+\mathrm{p}}{\mathrm{b}+\mathrm{p}}$ = $\frac{\mathrm{x}}{\mathrm{y}}$

⟹ x(a + p) = y(b + p)

⟹ ax + px = by + py

⟹ py – px = ax – by

⟹ p(y - x) = ax - by

⟹ p = $\frac{\mathrm{ax}-\mathrm{by}}{\mathrm{y}-\mathrm{x}}$

Therefore, the required number is $\frac{\mathrm{ax}-\mathrm{by}}{\mathrm{y}-\mathrm{x}}$.