Two metallic oxides contain $27.6\%$ and $30\%$ oxygen respectively. If the formula of first oxide is $M_3{O}_4$ that of second will be

Metallic content $M$ in oxide:

$100-27.6=72.4\%$

$100-30=70\%$

$72.4\%$of $M$ = $3$ mol of $M$

=$3/ 72.4 x 70$

=$2.90$mol of $M$

Similarly,

$27.6$% of $O$ = $4$ mol of $O$

=$4/27.6 x 30$

=$4.3$ mol of $O$

$2.90:4.34\sim 2:3$

Hence, the correct option is $M_2{O}_3$ D.