Percentages up and down are two different things.
So a level 6 barrack is 20% faster than a level 5.
But a level 5 barrack is only 16 2/3 % slower than a level 6 Barrack.
In the same way that 100 is 25% more than 80
but 80 is only 20% less than 100.
In your case it comes to (15m) 900 seconds - 16.66...% = 750 seconds (12m30s), but 750 seconds + 20% = 900 seconds.
So that's the answer to your question.
Your calculations are correct, your math however isn't, cos you did the calculations the wrong way.