Given that $P, Q$ and $R$ are consecutive odd numbers in ascending orders.
We can take $P = x,Q = x+2$ and $R = x+4$
According to the question$:3P = 2R – 3$
$\implies 3x = 2(x+4) – 3$
$\implies 3x = 2x + 8 – 3$
$\implies x= 5$
$\therefore R = x+4 = 5 + 4 = 9.$
So, the correct answer is $(C).$