Question : A number is increased by 5% and then the increased number is decreased by 5%. What is the net increase or decrease per cent?
Option 1: 0.25% decrease
Option 2: 0.75% increase
Option 3: 1% increase
Option 4: 0.50% decrease
Correct Answer: 0.25% decrease
Solution :
Let $x$ be the number.
Increase = 5%
Increased number = $x$ + 5% of $x$ = 105% of $x$ = $1.05x$
Decrease = 5%
Final number = $1.05x$ – 5% of $1.05x$ = $0.95×1.05x$ = $0.9975x$
Net decrease = $\frac{x – 0.9975x}{x}$ × 100 = $0.25$%
Hence, the correct answer is a 0.25% decrease.
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