**699** persons are there in building P and **513** persons are there in building Q.

With the following steps we can get the answer:

Let us take persons in Building P is A, and Q is B.

Then,

A - 93 = B + 93

So, B = A - 186 ----- (1)

Similiarly,

A + 109 = ( B - 109 ) * 2

So, 2B = A + 327 ---- (2)

Subtract (1) from (2)

2B = A + 327 -

B = A - 186

B = 0 + 513

Then, B put in to (1)

513 = A - 186

A = 513 + 186 = 699

Check the answer:

699 - 93 = 513 + 93 == 606

699 + 109 = (513 - 109) * 2 = 808