Final answer:
Nat's recognized gain is $45,000 and his basis for the lot is $75,000.
Step-by-step explanation:
To calculate Nat's recognized gain and basis for the lot, we need to determine the difference between the purchase price and the adjusted basis of the lot.
The recognized gain is the excess of the normal selling price over the adjusted basis. In this case, the normal selling price is $90,000 and the adjusted basis is $45,000. So, the recognized gain is $90,000 - $45,000 = $45,000.
The basis for the lot is the purchase price, which is $75,000.