AHSME 1970 Problem 35

A retiring employee receives an annual pension proportional to the square root of the number of years of his service. Had he served $a$ years more, his pension would have been $p$ dollars greater, whereas had he served $b$ years more $(b\ne a)$, his pension would have been $q$ dollars greater than the original annual pension. Find his annual pension in terms of $a,b,p$ and $q$. $\text{(A) } \frac{p^2-q^2}{2(a-b)} \text{(B) } \frac{(p-q)^2}{2\sqrt{ab}} \text{(C) } \frac{ap^2-bq^2}{2(ap-bq)} \text{(D) } \frac{aq^2-bp^2}{2(bp-aq)} \text{(E) } \sqrt{(a-b)(p-q)}$