"A is faster than B by 40%"

Question

I am trying to understand how to compare speeds in English. I have two types of devices that do the same thing. Their performances are measured in operations per second.

Let's say I have Device A that operates 17 times per second and device B that operates 12 times per second. Is it correct to say that:

Device A is faster than B by 41.7%?

because (17 - 12)/12 is approximately 0.417. How should it be (17 - 12)/17 = 0.294? That means the following is correct

Device A is faster than B by 29.4%?

Also I wonder what are some other ways I can say one device is more/less efficient than the other?

Answer 1

17 / 12 = 1.42 = "This device is 42% faster than that device."

12 / 17 = 0.71 = (1 - 0.29) = "This device is 29% slower than that device."

17 - 12 = 5 = "This device performs 5 operations per second more than that device."

12 - 17 = -5 = "This device performs 5 operations per second less than that device."

Answer 2

You asked about (17-12)/12 versus (17-12)/12.The convention is that the denominator is the value of the item being compared to, which in your examples is the one mentioned after the word "than". So in:

…A is [something] than B

A is being compared to B and so B goes on the denominator.

By contrast, you would put A in the denominator if the sentence was:

…B is [something] than A

One area to be careful with is when the quantities you are comparing are themselves percentages. So, suppose A=17% and B=12% were the profit percentages of two companies. Then strictly speaking we could still say that:

A is more profitable than B by 41.7%

but a common alternative is to say that:

A is more profitable than B by 5 percentage points

NOTE: in the first part of my answer, I focused on what goes on the denominator, and I ignored the order of items on the numerator. That's because we're usually looking for the absolute value (sign ignored), and the order doesn't matter for that. Of course it does matter when deciding whether to use "smaller" or "larger", say, but I'm assuming you get that already.