Given the ratio AP : AB = 3 : 7.Let AP = 3x and AB = 7x.We know that the total length of side AB is the sum of its segments AP and PB:AB = AP + PB7x = 3x + PBPB = 7x − 3x = 4xBy Basic Proportionality Theorem (BPT), since PQ || BC:$\; \frac{AP}{PB} = \; \frac{AQ}{QC}$$\; \frac{3x}{4x} = \; \frac{AQ}{QC}$$\; \frac{3}{4} = \; \frac{AQ}{QC}$Therefore, the ratio AQ : QC is 3 : 4.