Question : A's salary was decreased by 50% and subsequently increased by 50%. How much percent does he lose?
Option 1: $25\%$
Option 2: $50\%$
Option 3: $12\frac{1}{2}\%$
Option 4: $\text{No loss}$
Correct Answer: $25\%$
Solution :
Given: The salary of A was decreased by 50% and subsequently increased by 50%.
Let the salary of A be 100 units.
Salary was decreased by 50%, decreased salary = 100 –100 × $\frac{50}{100}$ = 50 units
Then, the salary was increased by 50%, increased salary = 50 + 50 × $\frac{50}{100}$ = 75 units
So, the final salary = 75 units
$\therefore$ Loss percentage $=\frac{\text{difference}}{\text{initial value}} × 100= \frac{(100–75)}{100}× 100 = 25\%$
Hence, the correct answer is 25%.
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