In the diagram below, we have PQ = 2AP = 2QB and AR/RC = 2/3. Find the ratio of the area of triangle BCQ to the area of triangle CQR.
Look at triangle(ABC) -- Drop a perpendicular from C to AB.
This will be the height of triangle(CQB) with base QB.
It will also be the height of triangle(CQA) with base AQ.
Since AQ = 3 x QB, the area of triangle(CQA) = 3 x area of triangle(CQB).
Look at triangleAQC) -- Drop a perpendicular from Q to AC.
This will be the height of triangle(QRA) with base RA.
It will also be the height of triangle(QRC) with base RC.
Since AR/RC = 2/3, the area of triangle(QRA) = 2/3 · area of triangle(QRC).
This means that triangle(QRC) = 3/5 the area of triangle(CQA).
Can you take it from here?