Calculating Selling Price with Profit and Loss Percentage

This problem involves finding the original cost price of an article when its selling price and loss percentage are known, and then calculating a new selling price required to achieve a specific profit percentage.

Step 1: Understand the Initial Situation

The shopkeeper sells an article for a certain price and incurs a loss. We are given:

• Initial Selling Price (SP1) = ₹46
• Loss Percentage = 8%

The selling price with a loss is calculated based on the cost price (CP). The formula is:

$\text{SP} = \text{CP} \times (1 - \frac{\text{Loss \%}}{100})$

Using the given values, we have:

$46 = \text{CP} \times (1 - \frac{8}{100})$

$46 = \text{CP} \times (1 - 0.08)$

$46 = \text{CP} \times 0.92$}

Step 2: Calculate the Cost Price (CP)

To find the cost price, we can rearrange the equation from Step 1:

$\text{CP} = \frac{46}{0.92}$

Let's perform the calculation:

$\text{CP} = 50$}

So, the cost price of the article is ₹50.

Step 3: Determine the Target Situation

The shopkeeper wants to gain a profit of 6%. We need to find the new selling price (SP2) for this target gain.

• Cost Price (CP) = ₹50 (calculated in Step 2)
• Target Profit Percentage = 6%

The selling price with a profit is calculated based on the cost price (CP). The formula is:

$\text{SP} = \text{CP} \times (1 + \frac{\text{Profit \%}}{100})$

Step 4: Calculate the New Selling Price (SP2)

Using the cost price and the target profit percentage, we can calculate the new selling price:

$\text{SP2} = 50 \times (1 + \frac{6}{100})$

$\text{SP2} = 50 \times (1 + 0.06)$

$\text{SP2} = 50 \times 1.06$}

$\text{SP2} = 53$}

Conclusion: Required Selling Price for Gain

To gain 6%, the shopkeeper should sell the article for ₹53.

Let's summarize the key values:

Revision Table: Profit and Loss Formulas

Additional Information on Profit and Loss Calculations

Profit and loss percentages are always calculated on the cost price unless otherwise specified. Understanding the relationship between Cost Price (CP), Selling Price (SP), Profit, and Loss is fundamental for solving these types of questions.

• Profit: Occurs when SP > CP. Profit = SP - CP.
• Loss: Occurs when SP < CP. Loss = CP - SP.
• Profit Percentage: $(\frac{\text{Profit}}{\text{CP}}) \times 100$
• Loss Percentage: $(\frac{\text{Loss}}{\text{CP}}) \times 100$

These formulas help convert between absolute profit/loss values and their percentage equivalents relative to the cost price of the article.