Think in powers of two as 2^1 (first day)

2^2(second day)

…

2^13

2^14

2^15

Now 1/4th of 2^15 is 2^15/2^2 (as 25% is 1/4=1/2^2) so, answer is 2^13 i.e. 13th day.

2^2(second day)

…

2^13

2^14

2^15

Now 1/4th of 2^15 is 2^15/2^2 (as 25% is 1/4=1/2^2) so, answer is 2^13 i.e. 13th day.