Initial equilibrium: 2 moles each of P2, Q2, PQ with K=[P2][Q2][PQ]2=44=1.
After adding 1 mole each of P2 and Q2: initial composition is (3,3,2). Reaction quotient Q=94<K, so reaction shifts right.
Let x moles of reactants combine:
(3−x)2(2+2x)2=1
2+2x=3−x
3x=1 → x=31
Final moles: P2=3−31=2.67, Q2=2.67, PQ=2+32=2.67