A shopkeeper allows `28%` discount on MP and earn `36 (4)/(11)%` profit. If profit earned is Rs. 1680, then find the amount of discount.

Options

A. Rs. 2800
B. Rs. 2400
C. Rs. 2450
D. Rs. 3500

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Profit Percentage
The profit percentage given is \(36 \frac{4}{11}\%\). We can convert this mixed fraction into an improper fraction:
\[ 36 \frac{4}{11} = \frac{36 \times 11 + 4}{11} = \frac{396 + 4}{11} = \frac{400}{11}\% \]

### Step 2: Set Up the Equation for Cost Price (CP)
Let the cost price be \(X\). According to the profit percentage, we can express the profit in terms of the cost price:
\[ \text{Profit} = \frac{400}{11}\% \text{ of } X = \frac{400}{1100} \times X = \frac{4}{11}X \]
Given that the profit earned is Rs. 1680, we can set up the equation:
\[ \frac{4}{11}X = 1680 \]

### Step 3: Solve for Cost Price (CP)
To find \(X\), we can rearrange the equation:
\[ X = 1680 \times \frac{11}{4} \]
Calculating this gives:
\[ X = 1680 \times 2.75 = 4620 \]

### Step 4: Calculate Selling Price (SP)
The selling price can be calculated as:
\[ \text{SP} = \text{CP} + \text{Profit} = 4620 + 1680 = 6300 \]

### Step 5: Calculate Mark Price (MP)
The shopkeeper allows a discount of \(28\%\) on the mark price. Therefore, the selling price can also be expressed in terms of the mark price:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{28}{100}\right) = \text{MP} \times \frac{72}{100} \]
Substituting the selling price:
\[ 6300 = \text{MP} \times \frac{72}{100} \]
Rearranging gives:
\[ \text{MP} = 6300 \times \frac{100}{72} \]

### Step 6: Calculate Mark Price (MP)
Calculating this gives:
\[ \text{MP} = 6300 \times \frac{100}{72} = 8750 \]

### Step 7: Calculate the Amount of Discount
The amount of discount can be calculated as:
\[ \text{Discount} = \text{MP} - \text{SP} = 8750 - 6300 = 2450 \]

### Final Answer
The amount of discount is Rs. 2450.

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