smc

Note the original pension as $k\sqrt{x}$, where $x$ is the number of years served. Then, based on the problem statement, two equations can be set up. $$k\sqrt{x+a}=k\sqrt{x}+p$$ $$k\sqrt{x+b}=k\sqrt{x}+q$$ Square the first equation to get $$k^{2}x+a{k}^2=k^{2}x+2pk\sqrt{x}+p^2.$$ Because both sides have $$k^{2}x$$, they cancel out. Similarly, the second equation will become $b{k}^2=q^2+2qk\sqrt{x}.$ Then, $a$ can be multiplied to the second equation and $b$ can be multiplied to the first equation so that the left side of both equations becomes $ab{k}^2$. Finally, by setting the equations equal to each other, $$b{p}^2+2bpk\sqrt{x}=a{q}^2+2aqk\sqrt{x}.$$ Isolate $k\sqrt{x}$ to get $\boxed{\frac{a{q}^2-b{p}^2}{2(bp-aq)}}=\frac{a{q}^2-b{p}^2}{2(bp-aq)}$.