A dealer buys a product at ₹ 1920, he sells at a discount of `20%` still he gets the profit of `20%`. What is the selling price of that product?

Options

A. ₹ 2304
B. ₹ 1536
C. ₹ 2200
D. it is not possible

Answer

To find the selling price of the product, we can follow these steps:

### Step 1: Calculate the Cost Price (CP)
Given that the dealer buys the product at ₹1920, we have:
- Cost Price (CP) = ₹1920

### Step 2: Calculate the Selling Price (SP) with Profit
The dealer makes a profit of 20%. To find the Selling Price (SP) when there is a profit, we use the formula:
\[ SP = CP + \text{Profit} \]
Where Profit can be calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]
Substituting the values:
\[ \text{Profit} = \frac{20}{100} \times 1920 = 0.2 \times 1920 = ₹384 \]
Now, substituting this back into the SP formula:
\[ SP = 1920 + 384 = ₹2304 \]

### Step 3: Account for the Discount
The dealer sells the product at a discount of 20%. Let the marked price (MP) be the price before the discount. The selling price after the discount can be expressed as:
\[ SP = MP - \text{Discount} \]
Where Discount is:
\[ \text{Discount} = \frac{20}{100} \times MP \]
Thus, we can rewrite the SP formula as:
\[ SP = MP - \frac{20}{100} \times MP = MP \times \left(1 - \frac{20}{100}\right) = MP \times 0.8 \]
Since we already calculated SP as ₹2304, we can set up the equation:
\[ 2304 = MP \times 0.8 \]

### Step 4: Solve for Marked Price (MP)
To find the marked price, we rearrange the equation:
\[ MP = \frac{2304}{0.8} \]
Calculating this gives:
\[ MP = 2880 \]

### Step 5: Conclusion
Thus, the selling price of the product after applying the discount is ₹2304.

### Summary of the Solution:
- Cost Price (CP) = ₹1920
- Profit = ₹384
- Selling Price (SP) = ₹2304
- Marked Price (MP) = ₹2880

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