Question

A number is increased by 10% and then it is decreased by 10%, then the net decrease percentage is:

• A. 1%
• B. 2%
• C. 5%
• D. 10%

Hint:

When a number is first increased by a percentage and then decreased by the same percentage, the net change is always less than the original percentage increase or decrease.

Answer 1

The Correct Option is A

Let the original number be \( N \). 
Step 1: After a 10\% increase, the new number becomes: \[ N' = N \times \left(1 + \frac{10}{100}\right) = N \times 1.10 \] 
Step 2: Now, after a 10\% decrease, the new number becomes: \[ N'' = N' \times \left(1 - \frac{10}{100}\right) = N \times 1.10 \times 0.90 = N \times 0.99 \] 
Step 3: The percentage decrease is: \[ \text{Percentage decrease} = \frac{N - N''}{N} \times 100 = \frac{N - 0.99N}{N} \times 100 = 1\% \] Thus, the net decrease percentage is 1%.