1970 AMC 12 Question 35 - thichhoctoan.com

Question 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 $q.$

$\dfrac{p^2-q^2}{2(a-b)}$
$\dfrac{(p-q)^2}{2\sqrt{ab}}$
$\dfrac{ap^2-bq^2}{2(ap-bq)}$
$\dfrac{aq^2-bp^2}{2(bp-aq)}$
$\sqrt{(a-b)(p-q)}$