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Difficulty: MediumProfit, Loss, and Markup

A store owner purchased a shipment of coats. She marked up the cost price of each coat by 40%40\% to set the regular selling price. During a clearance sale, she offered a discount of 15%15\% off the regular selling price on all remaining coats. If a coat was sold at the clearance price for $238\$238, what was the cost price of the coat?

  1. A
    $168.00\$168.00
  2. B
    $170.00\$170.00
  3. C
    $190.40\$190.40
  4. $200.00\$200.00Answer
  5. E
    $212.50\$212.50

Answer

The cost price of the coat was $200.00\$200.00.
The correct answer is $200.00\$200.00. The regular price is 140%140\% of the cost price (1.40C1.40C). A 15%15\% discount on the regular price means the clearance price is 85%85\% of the regular price, which translates to 0.85×1.40C=1.19C0.85 \times 1.40C = 1.19C. Setting 1.19C=$2381.19C = \$238 yields C=$200.00C = \$200.00.

Step-by-Step Solution

1
Define variables and express the regular selling price in terms of the cost price.
Let CC be the cost price of a coat. The regular selling price is R=C+0.40C=1.40CR = C + 0.40C = 1.40C.
Markup is calculated as a percentage of the cost price.
2
Express the clearance price in terms of the regular selling price and cost price.
The clearance price is R×(1−0.15)=1.40C×0.85=1.19CR \times (1 - 0.15) = 1.40C \times 0.85 = 1.19C.
The discount of 15%15\% is applied to the regular selling price, resulting in 85%85\% of the regular selling price.
3
Solve for the cost price CC using the given clearance price.
1.19C=238  ⟹  C=2381.19=2001.19C = 238 \implies C = \frac{238}{1.19} = 200.
Equating the algebraic expression for the clearance price to the given numerical value gives the original cost price.

Key Concept

Successive Percentage Changes in Profit and Loss
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Topics

Profit, Loss, and Markup

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