Is the answer A?

Rate of rockets/hr=

R(A)=x rockets/1hr
R(B)=1.1xrockets/hr

thus time to make 660 rockets=

t(A)=660/x
t(B)=660/1.1x

but we know that it takes machine A 10 hours more than it takes machine B, so:

t+10=660/x
t=660/1.1x

substitute and solve for x.

Work from options. However note that whatever number you use, a 10% increment must also divide 660. Again, note that the speed cannot be big since time taken will decrease and if that happens, you will not be able to get a 10Hour difference

If we consider A i.e. 6 to produce 660 it will take 110hours
A 10% increment means 6.6 and it will take 100hours to produce 660

Thus this satisfies the Question

So Speed of A = 6


Old Fashioned Way

Let Speed of A = X
Speed of B = 1.1X

(660/X) - (666/1.1X) = 10

thanks Neo. oftentimes i forget to work "backwards" from the answer choices. would have saved me a lot more time!