Percentage unchanged

Answer: 9.09090...% 

Using scale factors

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 Area is unchanged so ?% of 110% = 100%

$$\begin{array}{rl}\frac{?}{100}\times 110& =100\\ ?\times 110& =10000\\ ?\times 11& =1000\\ ?& =\frac{1000}{11}\text{ or }90.90909...\end{array}$$ So the width is decreased by $100-90.90909...=9.090909...\text{ or }\frac{100}{11}=9\frac1{11}$

Using algebra

The area of the original rectangle was $wb$

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The area of the altered rectangle is $pw \times 1.1b$

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Since the two areas are equal,

$1.1 pwb = wb$

so

$1.1 p = 1$

so $p = \frac{1}{1.1} = \frac{10}{11}$

So the width is $\frac{10}{11}$ of its original value, so it has been decreased by $\frac1{11}$, which as a percentage is $9$ and $\frac1{11}\%$, or $9.09\%$ to 2.d.p.