Sorry davidben1 but my brain is on vacation till the end of the year.
I am just too lazy to calculate and take leap years into an account.

60*24=1440 divided by 25=57.6 1000 divided by 57.6 = 17.3411111years

assuming leap years are included, average is about every 4 years, so we will add 250 extra days to our math problem to account for the 250 leap years in 1000 years and we all know a leap year is just one extra day in a year. so 365 days*1000 years=365,000 days plus the 250 so 365,250 days in 1000 years. 24 hours a day * 365,250 days = 8,766,000 total hours * 60 minutes an hour = 525,960,000 minutes in 1000 years. now we need to know how many minutes are just 1 day, 60min*24hr=1440 mins in a day. so now we make an equation. 25/1440=n/525,960,000. so cross multiply and you get 1440n=13,149,000,000. divide to find n. 13,149,000,000/1440. so 25 minutes equals 9,131,250 minutes in your construct. aka. 6341.1458333 days/7days=905.8779761905 weeks/4 weeks=226.4694940476 months/12 months=18.8724578373 years

everyone will disagree on the correct answer depending on how detailed you actually go into the math, for sake of time and confusion I went with the simplest answer

25mins = 32-36 yrs. Cal. Leap and other factors

That's what I got too...
1440 min in a day.
% 25 min is of it = x
x x 1k years = 17.3611111

Quick *rough* check.
Using rounded numbers.
There are 57.6 25 min periods in a day or say 50,
times answer of 17.361111 or say 20,
equals 1000...

But I didn't count leap years... Good call. :)

This didn't work.
I reposted the right way..

ScrumpyHaze

Relatively speaking... ;0

Does that day have 24h as well?

just a few conversions and maths inverse proportion.

this was a very clever question for the case that there might be a trick. i liked it :)

Simple conversion factors, assuming a 31 day month. The answer is 17 years, 4 months, 10 days and 8 hours.