Explanation

(d)
Percentage of element $M$ in $M_{2}O_{3} = 53$
Let the atomic mass of $M = x$
Mass of $M$in $M_{2}O_{3} = 2x$
Total atomic mass of $M_{2}O_{3} = 2x + 16 \times 3$
$= 2x + 48$
Percentage of an element
$= \frac{Mass\ of\ an\ element\ in\ a\ compound}{Total\ mass\ of\ compound} \times 100$
$53 = \frac{2x}{2x + 48} \times 100$
$53(2x + 48) = 200x$
$x = 27$