The removed amount must equal the added amount, so one third of the original water equals \(\displaystyle \frac14\) of full capacity.

The original water is three copies of that quarter: \(\displaystyle 3\times\frac14=\frac34\) of capacity. After one third is removed, two copies remain: \(\displaystyle 2\times\frac14=\frac12\).

Check: \(\displaystyle \frac13\times\frac34=\frac14\) is used and then replaced. The removal fraction refers to the original water; the addition fraction refers to the tank’s full capacity.

Answer

Initially \(\displaystyle \frac34\) of capacity; before the addition \(\displaystyle \frac12\) of capacity.