A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the actual price price were his was the listed price of the article?

Problem: Calculate Percent Above Cost for Listed Price

Given:

• Cash discount = 20%
• Profit = 20%
• Offers 16 articles for the price of 12 (i.e. sells 16 for price of 12)

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Step 1: Let the Cost Price per article = \( C \)

Step 2: Dealer makes 20% profit, so S.P. per article (normal) = \( 1.2 C \)

Step 3: But dealer gives 16 articles for price of 12, so effectively:

\[ \text{Effective S.P. per article} = \frac{12 \times \text{Listed Price per article} \times (1 - 0.20)}{16} \] Here, listed price per article = \( L \), and after 20% discount, price per article = \( 0.8 L \) So, \[ \text{Effective S.P. per article} = \frac{12 \times 0.8 L}{16} = 0.6 L \]

Step 4: Since effective S.P. per article = \(1.2 C\) (profit price), we have:

\[ 0.6 L = 1.2 C \implies L = \frac{1.2 C}{0.6} = 2 C \]

Step 5: The listed price \( L \) is 2 times the cost price \( C \), so:

\[ \text{Percent above cost} = \left( \frac{L - C}{C} \right) \times 100 = (2 - 1) \times 100 = 100\% \]

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Answer: The listed price was 100% above the actual cost price.