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Difficulty: MediumPercentage Calculations

A logistics facility implements an energy-saving program that reduces its daily electricity consumption by 20%20\%. Six months later, expanded operations require the facility to increase its new, reduced consumption by 30%30\%. What is the net percentage change in the facility's daily electricity consumption compared to the original amount?

  1. 4%4\% increaseAnswer
  2. B
    10%10\% increase
  3. C
    24%24\% increase
  4. D
    16%16\% decrease

Answer

The net change is a 4%4\% increase compared to the original electricity consumption.
To find the net percentage change, each change must be applied sequentially. A 20%20\% decrease leaves 80%80\% of the original amount. A subsequent 30%30\% increase is calculated on this 80%80\% (0.30×80%=24%0.30 \times 80\% = 24\%). Adding this to the reduced amount gives 80%+24%=104%80\% + 24\% = 104\%. The final amount is 104%104\% of the original, representing a 4%4\% net increase.

Step-by-Step Solution

1
Establish an initial baseline value to simplify calculations.
Assume the original daily electricity consumption is 100100 units.
Using 100100 makes percentage calculations intuitive and straightforward.
2
Calculate the consumption after the initial 20%20\% reduction.
100−(0.20×100)=80100 - (0.20 \times 100) = 80 units.
The facility reduces its original consumption by 20%20\%.
3
Calculate the final consumption after the subsequent 30%30\% increase.
80+(0.30×80)=80+24=10480 + (0.30 \times 80) = 80 + 24 = 104 units.
The 30%30\% increase must be applied to the new, reduced base of 8080 units, not the original 100100 units.
4
Determine the net percentage change from the original baseline.
104−100=+4104 - 100 = +4, which represents a 4%4\% increase.
Comparing the final amount (104104) to the original amount (100100) yields the exact net percentage change.

Key Concept

Successive Percentage Changes
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Topics

Percentage Calculations

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