A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is increased above the cost price by

Options

A. `40%`
B. `39%`
C. `50%`
D. `20%`

Answer

To solve the problem step-by-step, we will first define some variables and then use the information provided in the question.

### Step 1: Define Variables
Let:
- \( CP \) = Cost Price of one article
- \( MP \) = Marked Price of one article
- \( SP \) = Selling Price of one article after discount

### Step 2: Calculate Selling Price After Discount
The tradesman gives a 4% discount on the marked price. Therefore, the selling price after discount can be calculated as:
\[ SP = MP - (4\% \text{ of } MP) = MP - 0.04 \times MP = 0.96 \times MP \]

### Step 3: Calculate Total Selling Price for 15 Articles
Since the tradesman gives 1 article free for every 15 articles bought, when a customer buys 15 articles, they actually receive 16 articles. The total selling price for 15 articles is:
\[ \text{Total SP for 15 articles} = 15 \times SP = 15 \times (0.96 \times MP) = 14.4 \times MP \]

### Step 4: Calculate Total Cost Price for 15 Articles
The total cost price for 15 articles is:
\[ \text{Total CP for 15 articles} = 15 \times CP \]

### Step 5: Use Gain Percentage to Relate SP and CP
According to the problem, the tradesman gains 35%. This means:
\[ \text{Total SP} = \text{Total CP} + 35\% \text{ of Total CP} \]
\[ \text{Total SP} = 1.35 \times \text{Total CP} \]

Substituting the values we have:
\[ 14.4 \times MP = 1.35 \times (15 \times CP) \]

### Step 6: Simplify the Equation
Now we simplify the equation:
\[ 14.4 \times MP = 20.25 \times CP \]
\[ MP = \frac{20.25 \times CP}{14.4} \]

### Step 7: Calculate the Increase in Marked Price Above Cost Price
Now we need to find how much the marked price is increased above the cost price:
\[ MP - CP = \frac{20.25 \times CP}{14.4} - CP \]
\[ = \left(\frac{20.25}{14.4} - 1\right) \times CP \]
\[ = \left(\frac{20.25 - 14.4}{14.4}\right) \times CP \]
\[ = \left(\frac{5.85}{14.4}\right) \times CP \]

### Step 8: Calculate the Percentage Increase
To find the percentage increase in marked price above cost price:
\[ \text{Percentage Increase} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{5.85}{14.4}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Increase} \approx 40.625\% \]

### Final Answer
The marked price is increased above the cost price by approximately **40.63%**.

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