MathDB
Pension of a retiring employee

Source: 1970 AHSME Problem 35

April 16, 2014
AMC

Problem Statement

A retiring employee receives and annual pension proportional to the square root of the number of years of his service. Had he served aa years more, his pension would have been pp dollars greater, whereas, had he served bb years more bab\neq a, his pension would have been qq dollars greater than the original annual pension. Find his annual pension in terms of a,b,p,a,b,p, and qq.
<spanclass=latexbold>(A)</span>p2q22(ab)<spanclass=latexbold>(B)</span>(pq)22ab<spanclass=latexbold>(C)</span>ap2bq22(apbq)<spanclass=latexbold>(D)</span>aq2bp22(bpaq)<spanclass=latexbold>(E)</span>(ab)(pq)<span class='latex-bold'>(A) </span>\dfrac{p^2-q^2}{2(a-b)}\qquad<span class='latex-bold'>(B) </span>\dfrac{(p-q)^2}{2\sqrt{ab}}\qquad<span class='latex-bold'>(C) </span>\dfrac{ap^2-bq^2}{2(ap-bq)}\qquad<span class='latex-bold'>(D) </span>\dfrac{aq^2-bp^2}{2(bp-aq)}\qquad <span class='latex-bold'>(E) </span>\sqrt{(a-b)(p-q)}