A shopkeeper gives `18 (2)/(11)%` discount to his customer but he sells only smuggled goods and as a bribe he pays 12.5% on the CP. Find what should be the MP if he desires to make a profit of 37.5% and the CP of article is Rs. 3584?

Options

A. Rs. 4556
B. Rs. 5656
C. Rs. 6776
D. Rs. 8089

Answer

To solve the problem step by step, we need to calculate the required Mark Price (MP) based on the given conditions.

### Step 1: Calculate the Bribe Amount
The bribe is given as 12.5% of the Cost Price (CP).

Given:
- CP = Rs. 3584
- Bribe = 12.5% of CP

Calculation:
\[ \text{Bribe} = \frac{12.5}{100} \times 3584 = \frac{12.5 \times 3584}{100} = \frac{44800}{100} = Rs. 448 \]

### Step 2: Calculate the Total Cost Price
The total cost price is the sum of the original cost price and the bribe.

Calculation:
\[ \text{Total Cost Price} = CP + \text{Bribe} = 3584 + 448 = Rs. 4032 \]

### Step 3: Calculate the Selling Price for Desired Profit
The shopkeeper wants to make a profit of 37.5%.

To find the Selling Price (SP):
\[ \text{SP} = \text{Total Cost Price} + \text{Profit} \]
\[ \text{Profit} = 37.5\% \text{ of Total Cost Price} = \frac{37.5}{100} \times 4032 = \frac{37.5 \times 4032}{100} = Rs. 1512 \]
\[ \text{SP} = 4032 + 1512 = Rs. 5544 \]

### Step 4: Calculate the Effective Discount Rate
The discount given is \(18 \frac{2}{11}\%\).

Convert this to an improper fraction:
\[ 18 \frac{2}{11} = \frac{198 + 2}{11} = \frac{200}{11} \% \]

### Step 5: Calculate the Selling Price in terms of Mark Price
Let MP be the Mark Price. The selling price after discount is given by:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{200}{1100}\right) \]
\[ \text{SP} = \text{MP} \times \frac{900}{1100} \]

### Step 6: Set the Selling Price Equal to the Calculated SP
Now we set the calculated SP equal to the expression we derived for SP:
\[ 5544 = \text{MP} \times \frac{900}{1100} \]

### Step 7: Solve for Mark Price (MP)
Rearranging the equation to solve for MP:
\[ \text{MP} = \frac{5544 \times 1100}{900} \]
\[ \text{MP} = \frac{6098400}{900} = 6776 \]

### Final Answer
The Mark Price (MP) should be Rs. 6776.

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