The cost of manufacturing an item was ₹24,000, and 20% of it was spent on packaging and its shipment to a retailer. The manufacturer made a profit of 50%, while the retailer incurred a loss of 20% in selling it to a customer. At what price (in ₹) was the item sold by the retailer?

Options

A. 32400
B. 37664
C. 35268
D. 34560

Answer

To solve the problem step by step, we will calculate the total cost incurred by the manufacturer, the selling price after profit, and finally the selling price after the retailer's loss.

### Step 1: Calculate the Total Cost of Manufacturing
The cost of manufacturing the item is given as ₹24,000. Additionally, 20% of this cost is spent on packaging and shipment.

\[ \text{Packaging and Shipment Cost} = 20\% \text{ of } 24000 = \frac{20}{100} \times 24000 = 4800 \]

Now, we add this cost to the manufacturing cost:

\[ \text{Total Cost} = \text{Manufacturing Cost} + \text{Packaging and Shipment Cost} = 24000 + 4800 = 28800 \]

### Step 2: Calculate the Selling Price for the Manufacturer
The manufacturer makes a profit of 50% on the total cost.

\[ \text{Profit} = 50\% \text{ of } 28800 = \frac{50}{100} \times 28800 = 14400 \]

Now, we calculate the selling price for the manufacturer:

\[ \text{Selling Price (Manufacturer)} = \text{Total Cost} + \text{Profit} = 28800 + 14400 = 43200 \]

### Step 3: Calculate the Selling Price for the Retailer
The retailer incurs a loss of 20% when selling the item to the customer. First, we find the loss amount:

\[ \text{Loss} = 20\% \text{ of } 43200 = \frac{20}{100} \times 43200 = 8640 \]

Now, we calculate the selling price for the retailer after the loss:

\[ \text{Selling Price (Retailer)} = \text{Selling Price (Manufacturer)} - \text{Loss} = 43200 - 8640 = 34560 \]

### Final Answer
The price at which the item was sold by the retailer is **₹34,560**.

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