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I was reading a text book and came across the following interesting short-cut:

If two items are sold, each at $X$, one at a gain of $P\%$ and the other at a loss of $P\%$, then overall loss percentage $= P^2/100 \%$.

Can anyone please explain the underlying logic on the basis of which this shortcut works?

Thanks in advance!

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    It is not worth learning this shortcut - there are so many more useful things to know. But it may be worth working it out2011-06-18
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    @Henry thanks for the feedback. As mentioned in my question, I am more interested in knowing the underlying logic so that I can work out the problem anytime (in cases where I don't remember the short-cut)2011-06-18
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    Many financial advisers love this. If something goes up x%, then down x%, it is now worth (1+x%)(1-x%)=1-x^2/100%. The math is perfect, but the interpretations put on it are sometimes amazing.2011-06-19
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    "..... something goes up x%, then down x%, ......The math is perfect, but the interpretations put on it are sometimes amazing." One interpretation I that I always enjoy is that the **average gain** is $\frac{x\% + (-x\%)}{2} = 0\%$ and so the customer has broken even.2011-12-24

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