Simple Maths Question

[raphal]

Trying to represent the improvement on something an email to the business. We have a number of reports that used to generate in 45 seconds, that's now been improved to just 5 seconds.

The first person said the improvement was 80%
His boss changed it to show it as an improvement of 8x because it looks better.
While I calculate it's a decrease of 88.9% (which I could call an 'improvement'). If I was to do a times improvement though, I would say it was roughly a 4x times improvement (4.125) improvement.

What is the nX times improvement?

Assume 100 reports in 45 sec before improvement
i.e. 11.11 reports in 5 secs

Now after improvements you can do 100 reports in 5 secs.

So % of improvement is (100 - 11.11) *100/11.11 = ~ 800%