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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 $(C).$

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 $(C).$