# Tick (✓) the correct answer

Question:

A number is first increased by 10% and then reduced by 10%. The number

(a) does not change

(b) decrease by 1 %

(c) increases by 1 %

(d) none of these

Solution:

(b) decrease by 1 %

Let $x$ be the number.

A $10 \%$ increase will give a new number, $\frac{110}{100} x=\frac{11}{10} x$

The number is then reduced by $10 \%$.

The new number will be $\frac{90}{100}\left(\frac{11}{10} \mathrm{x}\right)=\frac{990}{1000} x=\frac{99}{100} x$

Difference $=\mathrm{x}-\frac{99}{100} \mathrm{x}=\frac{1}{100} \mathrm{x}$

Percentage of decrease $=\frac{1}{100} x \times \frac{1}{\mathrm{x}} \times 100=1 \%$
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