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The price of a product increases by 20% in the first year and then decreases by 10% in the second year. If the initial price is тВ╣8000, what is the final price after two years?
8400
8640
8800
8500
8640
Use effective percentage formula: x+y+100xyтАЛ. Here, 20тИТ10+10020├Ч(тИТ10)тАЛ=10тИТ2=8%. Simply find 108% of 8000: 8000├Ч1.08=8640.
Initial price = 8000. First year increase = 20%. Second year decrease = 10%.
Final┬аPrice=Initial┬аPrice├Ч(1+100r1тАЛтАЛ)├Ч(1тИТ100r2тАЛтАЛ)
Use effective percentage formula: x+y+100xyтАЛ. Here, 20тИТ10+10020├Ч(тИТ10)тАЛ=10тИТ2=8%. Simply find 108% of 8000: 8000├Ч1.08=8640.
Many students calculate the 10% decrease on the initial 8000 instead of the increased price (8000 + 20% = 9600), leading to an incorrect result.
Calculate price after first year
Applying a 20% increase to the initial price of 8000 gives the new price.
8000├Ч1.20=9600
Calculate price after second year
Applying a 10% decrease to the result of the first year (9600) gives the final price.
9600├Ч0.90=8640
Final verification
Comparing the calculated value to the provided options confirms the answer.
8640=8640
B is correct because the successive application of a 20% increase and a 10% decrease on 8000 results in 8640.
This concept is identical to Compound Interest calculations where the rate of interest changes annually. Always apply multipliers sequentially for efficiency.