Question:
Tick (✓) the correct answer:
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 $=\frac{1}{100} x \times \frac{1}{\mathrm{x}} \times 100=1 \%$