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Comment by brockf | Hacker News Reader

From the article: "I know a union that got a substantial pay raise because a politician did not understand that adding and then subtracting 20% gets you to another result from the one you started."

Wouldn't this be a pay decrease?

x * 1.2 = y

y * 0.8 < x

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I've been trying to work this one through. One possible solution, (using a hefty dose of mathematical illiteracy, that looks like one of those word problems that occasionally appears in Marilyn vos Savant's column):

  base salary: $100
  $100 * 1.2 = $120
  $120 * (1.2 * .8) = $115.2

("It's a 20% pay cut from our pay raise, that's why you have to multiply our pay raise with our pay cut.")

Technically he didn't say that it was the pay that was being added and subtracted. Perhaps it could have been something like, say, hours?

If a sum of money (S0) is increased with p percent then decreased with the same percent, the final sum (S2) will be:

   S2 = S0 * (100+p)/100 * (100-p)/100

A plot[1] of this equation will quickly show that as p increases, S2 decreases.

[1] http://www.wolframalpha.com/input/?i=%28100%2Bp%29%2F100+*+%...

True. 20% of y is larger than 20% of x (which is what was added to x to obtain y) because y is a larger number. Therefore subtracting 20% of y from y will give you some value smaller than x. Eg: 100 + 20% = 120; 120 - 20% = 96.

Not that anyone here needs an explanation :)

It would make sense if the amount in question was from a deduction from pay of some sort, tax, union fee deduction etc., rather than the pay itself.

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