Let's call the two numbers a and b. Three options here:

-choose numbers for a and b. Work out s, p and q, and plug these into each answer. If only one answer gives you your numbers a and b, it must be right. If two answers both give you the right numbers a and b, try again.

-we know the two numbers add to s. Well, try adding the numbers in each answer choice - the right answer has to give you s. Only D does.

-do the algebra:

a + b = s
a/b = p/q

So a = s - b, and a = pb/q, so s-b and pb/q must be equal:

pb/q = s - b
pb/q + b = s
b(p/q + 1) = s
b = s/[p/q + 1]
b = sq/(p + q)

from which D must be correct (no need to find a).