Say there are x teachers and y students in M and a teachers and b students in P. We want y / b.

The prompt gives us x/y = a/b, so we've got something to start with.

S1:

y = b + 10,000

Obvs not a ratio, so not sufficient.

S2:

x/y = 1/20, or x = 20y. This also tells us that a/b = 1/20, so a = 20b. This doesn't help us with y/b, though! (To illustrate, say we have 1 teacher and 20 students in P. We could have the same (1 and 20) in M, or we could have 100 and 2000, so we can't solve.

S1 + S2:

We've got

y = b + 10,000
a/b = 1/20
x/y = 1/20

So our ratio y/b = (b + 10,000)/b ... but we can't solve for b!

Thanks Rich and Matt!!