Rufus, Inc. and Hardy Company are negotiating a nontaxable exchange of business properties. Rufus's property has a $$50,000$ tax basis and a $$77,500$ FMV$.$ Hardy's property has a $$60,000$ tax basis and a $$90,000$ FMV$.$

a$.$ Which party to the exchange must pay boot to make the exchange work? How much boot must be paid?

b$.$ Assuming the boot payment is made, how much gain or loss will Rufus realize and recognize on the exchange, and what tax basis will Rufus take in the property acquired?

c$.$ Assuming the boot payment is made, how much gain or loss will Hardy realize and recognize on the exchange, and what tax basis will Hardy take in the property acquired?