A big drop is formed by coalescing 1000 small identical drops of...

Let radius of the small drop be $r$ and the radius of the big drop be $R$. Then, total volume will remain constant, therefore

$1000 \times \left[ρ\left(\dfrac{4}{3}\pi{r}^{3}\right)\right] = \dfrac{4}{3}\pi{R}^{3}ρ$

$⇒ R = 10r$

Initial total surface energy, ${E}_{1} = 1000 \times 4\pi{r}^{2} \times S$ and 

${E}_{2} = 4\pi ( 10r{)}^{2}S$

$⇒ \dfrac{{E}_{1}}{{E}_{2}} = \dfrac{10}{1}\text{Hence}, x = 10 .$