The Doubling Lily Pads

If $x$ is the total Lillies, then:

$2^{24} = \dfrac{x}{2}$ $\implies \color{#D61F06}{x = 2^{25}}$

Thus at the 25th day, the pond will be doubled

It is rather a simple question; it just needs a little math:

Suppose the pond had 2 lilies at the start, it would then mean that it would change to 4 on the second day, and eight on the third. In other words, we can say that the lilies are

Doubling in amount, which means that tomorrow, the $totallilies = 2l$ [ $l$ stands for the amount of lilies in the present]

If the pond could support $x$ lilies, and the pond now contains $\frac {x} {2}$ lilies, we can safely say that the pond is half-filled. As the lilies double in amount, tomorrow, we would be able to see that the full pond is filled tomorrow , with the lilies amount as $x$ .

If it took 24 days for the lilies to fill the pond upto $\frac {x} {2}$ , it would take 25 days for the lilies to be the amount equal to $x$ , which fills the full pond.

Everyday, the lily pads double. On the 24th day, it is half full. Then it doubles on the 25th day, so it is full on the 25th day because half-full plus half full equals full.