In which one of the following is pq=3 ?

The correct answer is Option (4) → \(3:p=q:1\)

In a proportion \(a:b=c:d\), the product of the extremes equals the product of the means: \(ad=bc\). Each option is turned into this form to find \(pq\).

• Option (1) \(2p:3=1:q\) — \(2p\times q=3\times1\), so \(\displaystyle pq=\frac{3}{2}\)

• Option (2) \(2:p=3q:1\) — \(2\times1=p\times3q\), so \(\displaystyle pq=\frac{2}{3}\)

• Option (3) \(3:p=q:2\) — \(3\times2=p\times q\), so \(pq=6\)

• Option (4) \(3:p=q:1\) — \(3\times1=p\times q\), so \(pq=3\), the value asked for