To check the principle of multiple proportions,a series of pure binary compounds $(P_m Q_n)$ were analyzed and their composition is tabulated below. The correct option$(s)$ is(are)

Compound	Weight $\%$ of $P$	Weight $\%$ of $Q$
$1$	$50$	$50$
$2$	$44.4$	$55.6$
$3$	$40$	$60$

$(A)$ If empirical formula of compound $3$ is $P_3 Q_4$,then the empirical formula of compound $2$ is $P_3 Q_5$.
$(B)$ If empirical formula of compound $3$ is $P_3 Q_2$ and atomic weight of element $P$ is $20$,then the atomic weight of $Q$ is $45$.
$(C)$ If empirical formula of compound $2$ is $PQ$,then the empirical formula of the compound $1$ is $P_5 Q_4$.
$(D)$ If atomic weight of $P$ and $Q$ are $70$ and $35$,respectively,then the empirical formula of compound $1$ is $P_2 Q$.

• A
  $A, B$
• B
  $A, C$
• C
  $A, D$
• D
  $B, C$