Solving the Jacket Profit Calculation Problem

This problem involves calculating the original cost price of a jacket for a wholesaler, given the profit percentages applied at two stages: from the wholesaler to the retailer and from the retailer to the customer. We are also given the final price paid by the customer.

Step-by-Step Solution

Let's denote the cost price of the jacket for the wholesaler as \(CP_{wholesaler}\).

Step 1: Wholesaler's Selling Price to Retailer

The wholesaler sells the jacket to the retailer at a profit of 5%. This means the selling price for the wholesaler (\(SP_{wholesaler}\)) is the cost price for the retailer (\(CP_{retailer}\)).

The formula for selling price with profit is: \(SP = CP + \text{Profit Percentage of } CP\)

So, \(SP_{wholesaler} = CP_{wholesaler} + 5\%\text{ of } CP_{wholesaler}\)

In mathematical terms:

\(CP_{retailer} = CP_{wholesaler} \times \left(1 + \frac{5}{100}\right)\)

\(CP_{retailer} = CP_{wholesaler} \times \left(1 + 0.05\right)\)

\(CP_{retailer} = 1.05 \times CP_{wholesaler}\)

Step 2: Retailer's Selling Price to Customer

The retailer sells the jacket to the customer at a profit of 10% on their cost price (\(CP_{retailer}\)). This selling price is the final price the customer pays.

The selling price for the retailer (\(SP_{retailer}\)) is given as ₹4,158.

Using the profit formula again:

\(SP_{retailer} = CP_{retailer} + 10\%\text{ of } CP_{retailer}\)

In mathematical terms:

\(SP_{retailer} = CP_{retailer} \times \left(1 + \frac{10}{100}\right)\)

\(SP_{retailer} = CP_{retailer} \times \left(1 + 0.10\right)\)

\(SP_{retailer} = 1.10 \times CP_{retailer}\)

Step 3: Substitute and Solve for the Wholesaler's Cost Price

We know that \(CP_{retailer} = 1.05 \times CP_{wholesaler}\) and \(SP_{retailer} = 4158\). Substitute the expression for \(CP_{retailer}\) into the equation for \(SP_{retailer}\):

\(4158 = 1.10 \times (1.05 \times CP_{wholesaler})\)

\(4158 = (1.10 \times 1.05) \times CP_{wholesaler}\)

Let's calculate the product \(1.10 \times 1.05\):

\(1.10 \times 1.05 = 1.155\)

Now, the equation becomes:

\(4158 = 1.155 \times CP_{wholesaler}\)

To find \(CP_{wholesaler}\), divide the customer's price by 1.155:

\(CP_{wholesaler} = \frac{4158}{1.155}\)

Performing the division:

\(CP_{wholesaler} = 3600\)

Therefore, the cost price of the jacket for the wholesaler was ₹3,600.

Let's verify this by working forward:

• Wholesaler's cost: ₹3,600
• Wholesaler's profit: 5% of ₹3,600 = \(0.05 \times 3600 = ₹180\)
• Wholesaler's selling price (Retailer's cost): \(3600 + 180 = ₹3,780\)
• Retailer's cost: ₹3,780
• Retailer's profit: 10% of ₹3,780 = \(0.10 \times 3780 = ₹378\)
• Retailer's selling price (Customer's price): \(3780 + 378 = ₹4,158\)

The calculated final price matches the price paid by the customer.

Result

The cost price of the jacket for the wholesaler was ₹3,600.

Revision Table: Profit Calculation Chain

Understanding how profit is calculated at each step in a supply chain is key to solving these types of problems.

• Profit is always calculated as a percentage of the cost price for that specific transaction stage.
• The selling price of one stage becomes the cost price for the next stage.

Additional Information: Percentage Increase

When an amount increases by a certain percentage, you can find the new amount by multiplying the original amount by (1 + percentage/100). For example, increasing a price by 5% is equivalent to multiplying the original price by (1 + 5/100) = 1.05.

In this problem, the wholesaler's price is increased by 5%, and then that resulting price is increased by 10% by the retailer. The final price reflects these successive percentage increases on the original wholesaler cost.

\(CP_{customer} = CP_{wholesaler} \times (1 + \text{Wholesaler Profit Rate}) \times (1 + \text{Retailer Profit Rate})\)

\(4158 = CP_{wholesaler} \times (1 + 0.05) \times (1 + 0.10)\)

\(4158 = CP_{wholesaler} \times 1.05 \times 1.10\)

\(4158 = CP_{wholesaler} \times 1.155\)

\(CP_{wholesaler} = \frac{4158}{1.155} = 3600\)