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Difficulty: HardPercentage Calculations

A supplier sells aircraft parts. A specific component is marked up by 60%60\% from its original manufacturing cost to establish a catalog price. Later, the supplier applies a 25%25\% discount to the catalog price for a bulk order. If the discounted bulk price of the component is $300\$300, what was its original manufacturing cost?

  1. A
    \$150
  2. B
    \$195
  3. \$250Answer
  4. D
    \$360

Answer

The original manufacturing cost was \$250.
To find the original cost, the successive percentage changes must be expressed as multipliers. A 60%60\% markup is a multiplier of 1.601.60, and a 25%25\% discount is a multiplier of 0.750.75. Multiplying these together gives a net multiplier of 1.201.20 (1.60×0.75=1.201.60 \times 0.75 = 1.20). This means the final bulk price is 120%120\% of the original cost. Since the final price is $300\$300, dividing this by 1.201.20 yields the original manufacturing cost of $250\$250.

Step-by-Step Solution

1
Translate the 60% markup into a decimal multiplier.
Catalog Price = 1.60×1.60 \times Cost.
A 60% increase means the new price is 100% + 60% = 160% of the original cost.
2
Translate the 25% discount into a decimal multiplier.
Bulk Price = 0.75×0.75 \times Catalog Price.
A 25% decrease means the customer pays 100% - 25% = 75% of the catalog price.
3
Combine the multipliers to find the net percentage effect on the original cost.
1.60×0.75=1.201.60 \times 0.75 = 1.20. The net price is 120% of the original cost.
Successive percentage changes are multiplicative, not additive.
4
Set up the equation with the given final price and solve for the original cost (CC).
1.20C=3001.20C = 300, which solves to C=300÷1.20=250C = 300 \div 1.20 = 250.
Dividing the final amount by the net multiplier isolates the starting amount.

Key Concept

Successive Percentage Changes and Reverse Percentages
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Topics

Percentage Calculations

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