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Difficulty: MediumPercentage Calculations

An aviation squadron reduces its weekly flight hours by 15%15\% to conserve fuel. If the new weekly flight schedule is 340340 hours, what was the original number of weekly flight hours before the reduction?

  1. 400Answer
  2. B
    391
  3. C
    289
  4. D
    40

Answer

The original number of weekly flight hours was 400.
The problem describes a reverse percentage scenario. Because the hours were reduced by 15%, the current 340 hours represent 85% (100% - 15%) of the original schedule. To find the original amount, you divide the current amount by the decimal form of the remaining percentage: 340 / 0.85 = 400.

Step-by-Step Solution

1
Determine what percentage the new hours represent compared to the original.
The new hours represent 100%−15%=85%100\% - 15\% = 85\% of the original hours.
A reduction of 15% means 85% of the original amount remains.
2
Set up an equation where the original hours are represented by the variable xx.
0.85x=3400.85x = 340
This translates the relationship into an algebraic equation to solve for the unknown original base.
3
Solve for xx by dividing both sides by 0.850.85.
x=3400.85=400x = \frac{340}{0.85} = 400
Isolating xx provides the original number of flight hours.

Key Concept

Reverse Percentage Calculations

Alternative Method

You can set this up as a proportion: 85100=340x\frac{85}{100} = \frac{340}{x}. Cross-multiply to get 85x=3400085x = 34000, and divide by 85 to find x=400x = 400.
Estimated Time:1m 0s
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Topics

Percentage Calculations

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