Understanding Profit and Selling Price Calculation

This question asks us to find the selling price of an item when we know its cost price and the profit percentage earned upon selling it. This is a basic concept in profit and loss calculations, which are common in mathematics and business.

Defining the Terms

• Cost Price (CP): The price at which an item is bought. In this case, the cost price is Rs. 60.
• Profit Percentage: The profit expressed as a percentage of the cost price. Here, the profit percentage is 25%.
• Selling Price (SP): The price at which an item is sold. We need to find this value.
• Profit: The amount gained when the selling price is greater than the cost price.

Calculating the Profit Amount

The profit amount can be calculated using the profit percentage and the cost price. The formula is:

$\text{Profit} = \left( \frac{\text{Profit Percentage}}{100} \right) \times \text{Cost Price}$

Let's plug in the given values:

$\text{Profit} = \left( \frac{25}{100} \right) \times 60$

$\text{Profit} = \left( \frac{1}{4} \right) \times 60$

$\text{Profit} = 15$

So, the profit earned is Rs. 15.

Calculating the Selling Price

The selling price is the sum of the cost price and the profit amount. The formula is:

$\text{Selling Price} = \text{Cost Price} + \text{Profit}$

Now, substitute the cost price (Rs. 60) and the calculated profit (Rs. 15):

$\text{Selling Price} = 60 + 15$

$\text{Selling Price} = 75$

Therefore, the selling price of the item is Rs. 75.

Step-by-Step Solution Summary

1. Identify the given values: Cost Price (CP) = Rs. 60, Profit Percentage = 25%.
2. Calculate the profit amount: Profit = (Profit Percentage / 100) $\times$ CP = (25 / 100) $\times$ 60 = Rs. 15.
3. Calculate the selling price: Selling Price (SP) = CP + Profit = 60 + 15 = Rs. 75.

Revision Table: Key Profit & Loss Formulas

Additional Information: Understanding Percentage Profit

Percentage profit is always calculated with respect to the cost price, unless explicitly stated otherwise. A 25% profit on Rs. 60 means that for every Rs. 100 of cost price, there is a profit of Rs. 25. Since the cost price is Rs. 60, which is 60/100 = 0.6 times Rs. 100, the profit will be 0.6 times Rs. 25, which is Rs. 15. This is consistent with our calculation.

Alternatively, we can directly calculate the selling price using the formula:

$\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$

$\text{Selling Price} = 60 \times \left(1 + \frac{25}{100}\right)$

$\text{Selling Price} = 60 \times \left(1 + 0.25\right)$

$\text{Selling Price} = 60 \times 1.25$

$\text{Selling Price} = 75$

Both methods yield the same selling price of Rs. 75.