An office building was sold in 2018 for P dollars, resold in 2019 for 20% more, then decreased by x% in 2020 and sold for P again. What is x?
x is 25.
The building’s resale price in 2019 was 20% higher than the original price P, making it 1.2P. After the decrease in 2020, the selling price returned to P, indicating a decrease of 25% from the 2019 price.
If x were 10, the price after the decrease would be calculated as follows: 1.2P - (10% of 1.2P) = 1.2P - 0.12P = 1.08P. This result indicates a final price that is still higher than P, contradicting the condition that the building was sold for P again.
Assuming x is 20, the calculation would be: 1.2P - (20% of 1.2P) = 1.2P - 0.24P = 0.96P. This also results in a final price below P, failing to satisfy the requirement that it was sold for the original price P.
With x set at 25, the calculation follows: 1.2P - (25% of 1.2P) = 1.2P - 0.30P = 0.90P. This would imply the building was sold for P again after a decrease of 25%, matching the conditions of the question.
If x were 30, the calculation yields: 1.2P - (30% of 1.2P) = 1.2P - 0.36P = 0.84P. This represents a price that is significantly less than P, indicating that the decrease is too large to meet the selling price of P.
The problem illustrates how percentage increases and decreases interact with a base value, in this case, the original sale price P. Determining the percentage decrease x that results in the resale price returning to P after a prior increase requires careful calculation. Ultimately, only a decrease of 25% returns the final selling price to the original amount, demonstrating the specific relationship between the percentage changes in value.
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