Concept:If a:b is the sub-duplicate ratio of c:d, then ba=dc.Explanation:Given q:p is the sub-duplicate ratio of q−x2:p−x2.So pq=p−x2q−x2.Square both sides: p2q2=p−x2q−x2.Cross-multiply: q2(p−x2)=p2(q−x2).Expand: q2p−q2x2=p2q−p2x2.Bring x2 terms to one side: −q2x2+p2x2=p2q−q2p.Factor x2 on left and pq on right: x2(p2−q2)=pq(p−q).Factor p2−q2=(p−q)(p+q): x2(p−q)(p+q)=pq(p−q).Assuming p=q, cancel (p−q): x2(p+q)=pq.Solve for x2: x2=p+qpq.Answer:x2=p+qpq, which matches option C.