Tick ( ) the correct answer in the following: A number is first i… - Vidyadip

MCQ

Tick $(\checkmark)$ the correct answer in the following: A number is first increased by $10\%$ and then reduced by $10\%.$ The number.

A
Does not change
✓
Decrease by $1\%$
C
Increases by $1\%$
D
None 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 $=\frac{1}{100}\text{x}\times\frac{1}{\text{x}}\times100=1\%$

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