Question 18. Maybe this solution is a little long, but still... I'll write, e.g., just ABC instead of "the area of ABC".

Lemma. AB / BP = 2.

Proof. Draw a line through R parallel to CB and let S be the intersection with AB. AR = RC => AS = SB; RQ = QP => SB = BP.

End proof.

Let PAC = 1. Then PRC = PRA = 1/2; CQR = CQP = 1/4. By lemma, CBA = 2 CBP = 2/3 => ARQB = 2/3 - 1/4 = 5/12. PQB = PRA - ARQB = 1/2 - 5/12 = 1/12. Finally, BQ / QC = BQP / PQC = (1/12) / (1/4) = 1/3.