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The price of a machine increased by 10% in the first year, then decreased by 20% in the second year, and increased again by 25% in the third year. If the original price was тВ╣80,000, what is the final price after these three changes?
82,000
85,000
88,000
90,000
88,000
Use the Ratio Method: Convert percentages to fractions (11/10, 4/5, 5/4). Multiply original price by the product of these ratios: 80,000├Ч(11/10)├Ч(4/5)├Ч(5/4)=80,000├Ч(11/10)=88,000.
Original Price = тВ╣80,000. Successive percentage changes: +10% (1st year), -20% (2nd year), +25% (3rd year).
PfinalтАЛ=PoriginalтАЛ├Ч(1+100r1тАЛтАЛ)├Ч(1тИТ100r2тАЛтАЛ)├Ч(1+100r3тАЛтАЛ)
Use the Ratio Method: Convert percentages to fractions (11/10, 4/5, 5/4). Multiply original price by the product of these ratios: 80,000├Ч(11/10)├Ч(4/5)├Ч(5/4)=80,000├Ч(11/10)=88,000.
Students often incorrectly add or subtract percentages directly (10% - 20% + 25% = 15%) instead of applying successive changes, which leads to wrong answers.
Convert percentage changes to multipliers
Convert the percentage values into multiplication factors: +10% becomes 1+0.10=1.1, -20% becomes 1тИТ0.20=0.8, and +25% becomes 1+0.25=1.25.
1.1├Ч0.8├Ч1.25=1.1
Calculate the final price
Multiply the original price of 80,000 by the combined multiplier calculated in the previous step.
80,000├Ч1.1=88,000
C is correct because the successive application of the percentage changes 1.1, 0.8, and 1.25 on the initial amount of 80,000 results in a final value of 88,000.
This concept of compounding is identical to Compound Interest calculations, where the percentage changes act as annual interest rates.