What type of relay will handle a 51 amp 10 hp motor and a 75 amp 15 hp motor?
What type of relay will handle a 51 amp 10 hp motor and a 75 amp 15 hp motor?


A very very very large one, by normal standards :-).
That is a substantial requirement and  needs a relay specialist to check what you are doing.  

What voltage are you using and is it AC or DC.
1 HP = 746 Watts, so 10 HP = 7460 Watts
V = W/I = 7460/ 51A = 146V.
Which may mean you have a 110 VAC system with an allowance for starting, or ...?

That spec will allow a reputable relay supplier to ask you whatever other questions are necessary to fine tune what they offer. Things like: 


AC or DC makes a HUGE difference. 
Voltage makes a difference. 
Whether you have any sort of on-line starter or if this IS the online starter makes a difference. 
Whether the motors start loaded or are run up to speed and then loaded can make a large difference. 
N/C or N/O operation makes some difference (which may not be intuitively obvious) 
Other ... the specialist will ask questions.


What is the application?  

Serious question: What sort of answer did you expect?.