A big drop is formed by coalescing 1000 small droplets of water....

Lets say radius of small droplets is $r$ and that of big drop is $R$. Total volume of the drops will remains unchanged. Therefore, 

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

$⇒ R = 10r$

Now, initial surface energy is, ${U}_{i} = 1000\left(4\pi{r}^{2}S\right)$ and the final surface energy is, 

${U}_{f} = 4\pi{R}^{2}S$

$= 100\left(4\pi{r}^{2}S\right)$

Clearly, ${U}_{f} = \dfrac{1}{10}{U}_{i}$.