Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6\tfrac{1}{4}$%
Option 3: increased by $6\tfrac{1}{4}$%
Option 4: increased by $6$%
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Correct Answer: decreased by $6\tfrac{1}{4}$%
Solution :
Given: A number is increased by 25%.
The resulting number is decreased by 25%.
Let the number be 100.
Increased by 25% = (100 + 25) = 125
125 is decreased by 25%, then it becomes = $125×\frac{75}{100}$ = $\frac{375}{4}$
So, the required decrease percentage $=(\frac{100-\frac{375}{4}}{100}) ×100$%
= $\frac{25}{4}$%
= $6\tfrac{1}{4}$%
Hence, the correct answer is 'decreased by $6\tfrac{1}{4}$%'.
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