Maybe it was the other way around:

25 minutes of the 1,000 years in relation to 1,000 years = 1 day

Every 4th year will be 256 days and all the others are 255 and 1/4 day (255.25 days).

1,000 ÷ 4 = 250

There are 250 instances where the number of days per year will become 256 and the rest are 255. (Note: the 1/4 day was added to the 256.)

250x256 = 64,000
750x255 = 191,250
1,000 years = 255,250 days

In a single day we have 24 hours which equates to 1,440 minutes.

Therefore:

1,000 years (367,560,000 minutes) = 1 day (1,440 minutes)

The question asked 25 minutes but without stating which is which. The answers given already is one part of the question and other is this:

If 367,560,000 minutes divided by 14,702,400 minutes is equal to 25 minutes, then

1,440 minutes divided by 14,702,400 is equal to 0.00009794319 minutes.

To summarize, it would only take 0.00009794319 of a minute or 0.000001632386 of a second for 25 minutes to pass in the 1,000 years = 1 day conversion ratio.