Windows 7: "Smart" Alloy Will Make Your Air Conditioner 175% More Efficient

No, thats wrong.

It is 175% MORE efficient than it already is, which means 1.75 more efficient... That makes it 70%.

~Lordbob

If I earn £40 per hour and get a 175% increase, I will now earn £110 per hour. If my increase is to £70 per hour, that's only a 75% rise.

It's always clearer when you put it in financial terms

That 70% is still a product of the initial number.
175% (MORE) efficient, initial efficiency suggestion was 40%, = 40 (100%) + 30 (75%) = 70%
70% + 40% (the original number - the percentages are additive) = 110%.

Seeing as how one cannot generate more than is put into a system (power in = power out), the above numbers just do not work.
I would venture to say this system (may) improve efficience by a given amount, but any real numbers have yet to be determined/realized.

40%= 4/10= 0.4
175% = 175/100 = 1.75

.4 * 1.75 = 0.7 = 70%

another example.

Bob works at a job at 40% capacity.
Sue works twice as hard (200%)
sue works at 80% capacity

.4 * 2.0 = .80 or 80%

I would bet that it's 99% probable that the phrase "more efficient" was incorrectly used in the original source. Actual grammar is completely non-existant in most news sources these days.

By your analysis, a 100% increase would be worthless:

40%= 4/10= 0.4
100% = 100/100 = 1.00
.4 * 1.00 = 0.4 = 40%

So a 100% increase from 40% would be...still 40%. This is clearly wrong.

What's more, a 50% increase by this method would mean a decrease:

40%= 4/10= 0.4
50% = 50/100 = 0.5
.4 * 0.5 = 0.2 = 20%

We started with 40%, increased it by half, and ended up with... only 20%. This is even more clearly wrong.

A 25% increase from 40% is 50%; a 50% increase from 40% is 60%; a 100% increase from 40% is 80%; and a 175% increase from 40% is 110%. So either standard air conditioners generally work at rather low efficiencies and the new system is going to improve them by an absolutely astonishing amount, or this "175% increase" they quote is a mistake. My money is on option 2

I would agree with option 2 also.

No, you are still wrong.

50% is 1/2 correct?
So 1/2 of 50% is 25%.
175% is 7/4, so 7/4 of 50% is 87.5%

~Lordbob

You're missing the big point: This is on top of the original figure (added to).

so 175% more than 40% is 110%

let's work with actual numbers, shall we?

say (as in previous example) 100% is 100 units.
40% of this is 40 units.
still with me?

we increase the 40 units by 175% (175% of the 40 units).
first off, what are we doing?
we are adding an additional 175% of these 40 units to this amount.
40 * 1.75 (we all agree here 1.75 = 175%) = 70 (can be checked with a calculator for those who are slower)
this is the amount we are adding to the original 40 units.
so:
original units + 175% of those units = new total units
40 + 70 = 110 units now total.