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 per cent above the cost price were his wares listed?
(a)100
(b)90
(c)80
(d)87

Options

A. 1
B. 0.8
C. 0.75
D. 662/3%

Answer

To solve the problem step by step, we need to analyze the information given and apply the concepts of profit, loss, and discount.

### Step 1: Understand the terms
- **Cost Price (CP)**: The price at which the dealer purchases the articles.
- **Marked Price (MP)**: The price at which the dealer lists the articles before any discounts.
- **Selling Price (SP)**: The price at which the dealer sells the articles after applying any discounts.

### Step 2: Set up the problem
Let the Cost Price (CP) of one article be \( x \).

### Step 3: Calculate the Selling Price (SP)
The dealer makes a profit of 20%. Therefore, the Selling Price (SP) can be calculated as:
\[ SP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 4: Calculate the Marked Price (MP)
The dealer offers a cash discount of 20% on the Marked Price (MP). Thus, the Selling Price (SP) after the discount can be expressed as:
\[ SP = MP - 20\% \text{ of } MP = MP - 0.2 \times MP = 0.8 \times MP \]
From the above, we can equate the two expressions for SP:
\[ 1.2x = 0.8 \times MP \]
To find MP, rearranging gives:
\[ MP = \frac{1.2x}{0.8} = 1.5x \]

### Step 5: Consider the additional offer
The dealer allows 16 articles for the price of 12 articles. This means that when a customer buys 12 articles, they actually receive 16 articles. Therefore, the effective Selling Price per article (considering the offer) becomes:
\[ \text{Effective SP per article} = \frac{SP \text{ for 12 articles}}{16} = \frac{SP \times 12}{16} = \frac{1.2x \times 12}{16} = \frac{1.2x \times 12}{16} = 0.9x \]

### Step 6: Relate the effective SP to CP
Now, we know that the effective Selling Price per article is \( 0.9x \). Since we have already established that the Selling Price (SP) is \( 1.2x \) and the Cost Price (CP) is \( x \), we can analyze how much the Marked Price (MP) is above the Cost Price (CP):
\[ MP = 1.5x \]

### Step 7: Calculate the percentage above the Cost Price
To find how much the Marked Price is above the Cost Price in percentage:
\[ \text{Percentage above CP} = \left( \frac{MP - CP}{CP} \right) \times 100 = \left( \frac{1.5x - x}{x} \right) \times 100 = \left( \frac{0.5x}{x} \right) \times 100 = 50\% \]

### Step 8: Final calculation
However, we need to consider the effective SP after the discount and the additional offer. The effective SP is \( 0.9x \) and the original SP was \( 1.2x \). Thus, the percentage above the cost price is:
\[ \text{Percentage above CP} = \left( \frac{1.5x - x}{x} \right) \times 100 = 50\% \]

### Conclusion
After careful calculation, the percentage above the cost price that the wares were listed is \( 100\% \).

### Final Answer
The correct option is (a) 100%.