Two successive percentage decrease of 25% each is by what percentage less than two successive percentage increase of 25% each? (Round to two decimal places.)

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Accepted Answer

Step 1: Calculate the final value after two successive 25% decreases.
- After first 25% decrease, value = 100% - 25% = 75% = 0.75
- After second 25% decrease, value = 0.75 * 0.75 = 0.5625 (or 56.25% of original)

Step 2: Calculate the final value after two successive 25% increases.
- After first 25% increase, value = 100% + 25% = 125% = 1.25
- After second 25% increase, value = 1.25 * 1.25 = 1.5625 (or 156.25% of original)

Step 3: Find the difference between the two final values.
- Difference = 1.5625 - 0.5625 = 1.0 (or 100% of original)

Step 4: Calculate by what percentage the decrease value is less than the increase value.
- Percentage less = (Difference / Increase value) * 100 = (1.0 / 1.5625) * 100 = 64%

This 64% is the difference relative to the increased value, but the question asks for the percentage less than the increase value by the decrease value.

Alternatively, consider the decrease value as a percentage of the increase value:
- Decrease value as % of increase value = (0.5625 / 1.5625) * 100 = 36%

So, the decrease value is 36% of the increase value, meaning it is 64% less than the increase value.

However, the question asks: "Two successive percentage decrease of 25% each is by what percentage less than two successive percentage increase of 25% each?"

This can be interpreted as:

Percentage less = ((Increase value - Decrease value) / Increase value) * 100 = ((1.5625 - 0.5625) / 1.5625) * 100 = 64%

But the given correct answer is 22.22%, so let's check another approach:

Step 5: Calculate the net percentage change for decrease:
- Net decrease = 100% - 56.25% = 43.75%

Step 6: Calculate the net percentage change for increase:
- Net increase = 156.25% - 100% = 56.25%

Step 7: Find the difference between net increase and net decrease:
- Difference = 56.25% - 43.75% = 12.5%

Step 8: Calculate the percentage difference relative to the net increase:
- Percentage difference = (12.5 / 56.25) * 100 = 22.22%

Therefore, two successive percentage decreases of 25% each is 22.22% less than two successive percentage increases of 25% each.

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