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  4. A man's salary is increase by 10 %. In order to have his salary back to the original amount, it must be reduced by x % then value of x is

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Q. A man's salary is increase by $10 \%$. In order to have his salary back to the original amount, it must be reduced by $x \%$ then value of $x$ is

Percentages

Solution:

Let original salary $=x$
$10 \%$ increase in $x$ becomes
$x+\frac{10}{100} \times x=1.1 x$
Then, let decrease be $\mathrm{p} \%$
[1.1 $x$ becomes $1.1 x-\frac{p}{100} \times 1.1 x$ ]
$ \Rightarrow 1.1 x-\frac{P}{100} \times 1.1 x=x $
$ \Rightarrow 1.1 x \frac{(100-p)}{100}=x$
$\Rightarrow 1.1(100-p)=100 $
$\Rightarrow 110-1.1 \mathrm{p}=100$
$\Rightarrow 1.1 \mathrm{p}=10 $
$\Rightarrow p=\frac{10}{1.1}=\frac{100}{11}=9 \frac{1}{11}$