Solution:-
From the figure,
PQ || AC, AP = 4 cm, PB = 6 cm and BC = 8 cm
∠BQP = ∠BCA … [because alternate angles are equal]
Also, ∠B = ∠B … [common for both the triangles]
Therefore, ∆ABC ~ ∆BPQ
Then, BQ/BC = BP/AB = PQ/AC
BQ/BC = 6/(6 + 4) = PQ/AC
BQ/BC = 6/10 = PQ/AC
BQ/8 = 6/10 = PQ/AC … [because BC = 8 cm given]
Now, BQ/8 = 6/10
BQ = (6/10) ×8
BQ = 48/10
BQ = 4.8 cm
Also, CQ = BC – BQ
CQ = (8 – 4.8) cm
CQ = 3.2cm
Therefore, CQ = 3.2 cm and BQ = 4.8 cm