MCQ
Tick $(\checkmark)$ the correct answer in the following: A number is first increased by $10 \%$ and then reduced by $10 \%$. The number.
- ADoes not change
- ✓Decrease by $1 \%$
- CIncreases by $1 \%$
- DNone of these
✓
Answer
Correct option: B.
Decrease by $1 \%$
Let $x$ be the number.
A $10 \%$ increase will given a new number, $\frac{100}{100}\text{x}=\frac{11}{10}\text{x}$
The number is then reduced by $10 \%$.
The new number will be $\frac{90}{100}\Big(\frac{11}{10}\text{x}\Big)=\frac{990}{1000}\text{x}=\frac{99}{100}\text{x}$
Difference $=\text{x}-\frac{99}{100}\text{x}=\frac{1}{100}\text{x}$
Percentage of decrease $=\frac{1}{100}\text{x}\times\frac{1}{\text{x}}\times100=1%$
A $10 \%$ increase will given a new number, $\frac{100}{100}\text{x}=\frac{11}{10}\text{x}$
The number is then reduced by $10 \%$.
The new number will be $\frac{90}{100}\Big(\frac{11}{10}\text{x}\Big)=\frac{990}{1000}\text{x}=\frac{99}{100}\text{x}$
Difference $=\text{x}-\frac{99}{100}\text{x}=\frac{1}{100}\text{x}$
Percentage of decrease $=\frac{1}{100}\text{x}\times\frac{1}{\text{x}}\times100=1%$
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