percentage increase in performance

Question

What is :

1. by how much
2. to how much

efficiency of algorithm is increased , if

Initially it was executing in 20 seconds, after improvement (Final Time) it is executing only in 5 seconds. My Try:

1. by how much : (Initial Time - Final Time)
                 --------------------------- * 100
                    Initial Time  
2. to how much : Initial Time
                 ------------- * 100
                  Final Time

tell me if i'm wrong?

Answer 1

You've got the right idea, and perhaps I'm splitting hairs, but I think we could also swap the equations:

That is, the improvement increases performance by $$\frac{\text{initial time}}{\text{final time}}\times 100\% = 400\%.$$

The change leads to a $$ \frac{\text{initial time} - \text{final time}}{\text{initial time}}\times 100\% = 75\%$$ improvement in performance.

(perhaps you can clarify exactly how "by" and "to" are to be understood)