The packing fraction of equilateral triangular iron plates staked as shown below is$\frac{X}{Y}$ . Then $(X+Y)$  Value is
 
 

 $\frac{X}{Y}=\frac{2}{3}$
Each small equilateral triangular void formed by 3 big equilateral triangular plates. So each equilateral triangular void shared equally by three big equilateral triangular plates. Around each equilateral triangular plate, 6 small equilateral triangular void present.
$\therefore$ Number of equilateral triangular voids per each plate $=6\times \frac{1}{3}=2$
If edge length of triangular plate is a, edge length of triangular void will be  $\frac{a}{2}$.
Pack Fraction $=\frac{\frac{\sqrt{3}}{4}{a}^2}{\frac{\sqrt{3}}{4}{a}^2+2\times \frac{\sqrt{3}}{4}{\left(\frac{a}{2}\right)}^2}=\frac{1}{ }=\frac{2}{3}$