An engine with a brake horsepower of 20 bhp would have a rated horsepower of

hi your question is incomplete because you didn't give a value for the power losses. hence i will just give you the relationship between brake horsepower and rated horsepower

the relationship is this:  Hp (rated horse power) = BHP ( brake horsepower) - (power losses)

assuming a power loss of  10. the rated horse power will be = 20 - 10

10 hp

Explanation:

brake horsepower is the input horsepower of a system before power losses occur in the system like with a vehicle, the losses are caused mainly by the gear box, alternator, steering pump and the others

rated horsepower is the output horsepower of a system i.e the power needed to drive an engine continuously without failure after the power losses have been considered and taken out of the brake horsepower.