A dealer marked the price of an item 40% above the cost price. Once he gave successive discounts of 20% and 25% to a particular customer. As a result, he incurred a loss of ₹448. At what price did he sell the item to the mentioned customer?

Options

A. ₹2416
B. ₹2352
C. ₹2268
D. ₹2152

Explanation

To solve the problem step by step, we will first define the variables and then calculate the selling price after applying the discounts.

### Step 1: Define the Cost Price (CP)
Let the cost price of the item be \( CP \).

### Step 2: Calculate the Marked Price (MP)
The marked price is 40% above the cost price. Therefore, we can express the marked price as:
\[ MP = CP + 0.4 \times CP = 1.4 \times CP \]

### Step 3: Apply the First Discount
The dealer gives a discount of 20% on the marked price. The selling price after the first discount can be calculated as:
\[ SP_1 = MP - (20\% \text{ of } MP) = MP - 0.2 \times MP = 0.8 \times MP \]
Substituting the value of \( MP \):
\[ SP_1 = 0.8 \times (1.4 \times CP) = 1.12 \times CP \]

### Step 4: Apply the Second Discount
Next, the dealer gives a discount of 25% on the price after the first discount. The selling price after the second discount can be calculated as:
\[ SP_2 = SP_1 - (25\% \text{ of } SP_1) = SP_1 - 0.25 \times SP_1 = 0.75 \times SP_1 \]
Substituting the value of \( SP_1 \):
\[ SP_2 = 0.75 \times (1.12 \times CP) = 0.84 \times CP \]

### Step 5: Calculate the Loss
According to the problem, the dealer incurs a loss of ₹448. The loss can be expressed as:
\[ Loss = CP - SP_2 \]
Substituting the value of \( SP_2 \):
\[ 448 = CP - 0.84 \times CP \]
This simplifies to:
\[ 448 = 0.16 \times CP \]

### Step 6: Solve for the Cost Price (CP)
To find the cost price, we can rearrange the equation:
\[ CP = \frac{448}{0.16} = 2800 \]

### Step 7: Calculate the Selling Price (SP)
Now that we have the cost price, we can find the selling price \( SP_2 \):
\[ SP_2 = 0.84 \times CP = 0.84 \times 2800 = 2352 \]

### Final Answer
The price at which the dealer sold the item to the customer is ₹2352.

---