how did they arrive at $18\mathrm{.}9,27\mathrm{.}9$ and $31\mathrm{.}0$

LIFO liquidation gain $($pre$-$tax$)$: Year $11=18\mathrm{.}9/(1-\mathrm{.}34)=28\mathrm{.}6$; Year $10=27\mathrm{.}9/(1-\mathrm{.}34)=42\mathrm{.}3$;

Year $9=31\mathrm{.}0/(1-\mathrm{.}34)=47\mathrm{.}0$