Why Does 600/0.95 Differ from 600×1.05 When Calculating 95% Efficiency Loss?

This has been driving me a little crazy for quite some time now. I am almost embarassed to ask, but this just doesn't make sense to me. Can someone explain to me why 600 divided by 0.95 (600/0.95) and 600 multiplied by 1.05 (600*1.05) are not the same value?

If something is 95% efficient, then 5% is lost. So if I have a 600W load and 5% of my power is lost due to resistance in the power lines, I have to add 5% to my system to deliver the full 600W. What am I missing here? Please help.

Note that 1.05 is not the reciprocal of 0.95; The reciprocal of 0.95 to five significant digits is 1.0526.

The example in the first paragraph is not the same as the second paragraph.

Maybe this helps...

efficiency (n) = Pout/Pin

Therefore, Pin = Pout/n

Therefore, if Pout is 600 W and the efficiency is 95%, then the input power, Pin will be 600/0.95 = 631.58 W, so you need to add 31.58 W to the input to get 600 W from your device. Which means 31.58 W represents the loss.

I agree with the answers above, but wanted to point out the flaw in your reasoning

*So if I have a 600W load and 5% of my power is lost due to resistance in the power lines, I have to add 5% to my system to deliver the full 600W.*

Remember that what you add to the input will also experience the 5% loss, so you want:

0.95 x (amount I need to add) = 5% or (amount I need to add) = 5%/0.95 = 5.26%
Which is what David's and Rohit's answers are demonstrating