Understanding the Profit Calculation for Cold Drink Bottles

This problem asks us to find the selling price per bottle required for a shopkeeper to make a 20% profit on the total purchase cost of cold drink bottles.

Analyzing the Purchase Cost

The shopkeeper bought six small cold drink bottles for a total cost of ₹100.

• Total Cost Price (CP) for 6 bottles = ₹100
• Number of bottles purchased = 6

Calculating the Desired Total Selling Price (SP)

The shopkeeper wants to achieve a profit of 20% on the total cost price. The formula to calculate the Selling Price (SP) when a profit percentage is known is:

SP = CP + Profit

Profit is calculated as a percentage of the Cost Price:

\(\text{Profit} = \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{CP}\)

So, the Selling Price formula can also be written as:

\(\text{SP} = \text{CP} + \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{CP}\)

\(\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)\)

In this case:

• CP = ₹100
• Profit Percentage = 20%

Let's calculate the total selling price needed for the six bottles:

\(\text{Total SP} = ₹100 \times \left(1 + \frac{20}{100}\right)\)

\(\text{Total SP} = ₹100 \times \left(1 + 0.20\right)\)

\(\text{Total SP} = ₹100 \times 1.20\)

\(\text{Total SP} = ₹120\)

So, the shopkeeper needs to sell all six bottles for a total of ₹120 to get a 20% profit.

Finding the Selling Price Per Bottle

The total selling price of ₹120 is for the six bottles. To find the selling price for one cold drink bottle, we need to divide the total selling price by the number of bottles.

\(\text{SP per bottle} = \frac{\text{Total SP}}{\text{Number of bottles}}\)

\(\text{SP per bottle} = \frac{₹120}{6}\)

\(\text{SP per bottle} = ₹20\)

Therefore, the shopkeeper should sell one cold drink bottle for ₹20 to achieve a 20% profit on the initial purchase cost.

Conclusion

To make a 20% profit on the purchase of six cold drink bottles bought for ₹100, each bottle must be sold for ₹20.

Revision Table: Cost, Profit, and Selling Price

Here is a quick summary of the key terms used in this profit calculation problem:

Additional Information on Profit and Loss

Profit and loss calculations are fundamental concepts in business and commerce. They help determine the financial outcome of a transaction.

• Calculating Profit: If you sell something for more than you bought it, you make a profit. The difference is your profit amount.
• Calculating Loss: If you sell something for less than you bought it, you incur a loss. The difference is your loss amount.
• Percentage Calculations: Profit and loss are often expressed as a percentage of the cost price. This gives a standard way to compare profitability across different items or transactions, regardless of their actual cost.
• Markup: Sometimes, profit is referred to as 'markup', especially when calculating the selling price by adding a percentage directly to the cost price. A 20% profit on CP means a 20% markup on CP.

Understanding these basics is crucial for solving problems involving buying and selling, like the cold drink bottle example.