If 45% of P = 3/4 of Q, then P : Q is :

45% of P = $\frac{3}{4}$ of Q

$\frac{45}{100}$ × P = $\frac{3}{4}$ × Q

$\frac{9}{20}$ × P = $\frac{3}{4}$ × Q

$\frac{P}{Q}$ = $\frac{3}{4}$ × $\frac{20}{9}$

$\frac{P}{Q}$ = $\frac{5}{3}$

Hence,

P : Q = 5 : 3