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The Price of A is twice that of another fan B. The price of A is increased by 10% and that of B is decreased by 20%. Find the percentage decrease in the sum of the prices of the fans.

I am fighting myself to solve this one.

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    $\begingroup$ $2B\times1.10+B\times0.80=2B+B$, no change. $\endgroup$
    – user65203
    Oct 9, 2017 at 10:28

2 Answers 2

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$a=2b$ suppose $a=\$200;\;b=\$100$ sum is $\$300$

$a\to a+10\%\,a=\$220$

$b\to b-20\%\,b=\$80$

The sum is $\$300$ and is unchanged

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Set the price of fan B to $x$. The price of fan A is $2x$. The sum of those prices is $3x$. Now the prices change: the new price of A is $2x * 1.1 = 2.2x$. The new price of B is $x * 0.8 = 0.8x$. The sum of those new prices is $2.2x + 0.8x = 3x$, so the price of the sum doesn't change, so the percentage decrease in sum of the prices of the fans is $0\%$.

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