Question

What is percentage profit in selling an article at a discount of \(20 \%\) which was earlier being sold at a \(40 \%\) profit? (a) \(20 \%\) (b) \(14 \%\) (c) \(28 \%\) (d) \(12 \%\)

Short answer

a) 8% b) 10% c) 11% d) 12% Answer: d) 12%

Step-by-step solution

Understand the problem and identify the given values

We are given that an article was initially sold at a \(40 \%\) profit and then sold at a \(20 \%\) discount. We need to find the percentage profit in the second case. Let's assume the cost price of the article to be "C" (in dollars).

Calculate the initial selling price (with \(40 \%\) profit)

To find the initial selling price, we need to consider the \(40 \%\) profit. The formula to calculate that is: Initial Selling Price = \(C + (40 \% \text{ of } C)\) Initial Selling Price = \(C + (0.4 \times C)\) Initial Selling Price = \(C (1 + 0.4)\) Initial Selling Price = \(1.4C\)

Calculate the discounted selling price (with \(20 \%\) discount)

Now, we need to calculate the selling price after applying the \(20 \%\) discount on the initial selling price. Discounted Selling Price = Initial Selling Price \(- (20 \% \text{ of Initial Selling Price})\) Discounted Selling Price = \(1.4C - (0.2 \times 1.4C)\) Discounted Selling Price = \(1.4C - 0.28C\) Discounted Selling Price = \(1.12C\)

Find the profit and calculate the percentage profit

Now we'll find the profit made in the second case. Profit = Discounted Selling Price \(- C\) Profit = \(1.12C - C\) Profit = \(0.12C\) To find the percentage profit, we'll use the formula: Percentage Profit = \(\frac{Profit}{Cost \text{ Price}} \times 100\) Percentage Profit = \(\frac{0.12C}{C} \times 100\) The cost price "C" cancels out, leaving us with: Percentage Profit = \(12 \%\)

Identify the correct option from the given choices

Now we can see that the percentage profit in selling the article at a discount of \(20 \%\) after being sold at a \(40 \%\) profit is \(12 \%\). So the correct answer is (d) \(12 \%\).

Key concepts

Profit Calculation

When it comes to calculating profit, especially in the context of buying and selling, understanding the basic formula is key. Profit refers to how much more money you gain by selling an item compared to how much it costs to produce or buy it. In this particular exercise, you're given an initial percentage profit of 40%. This means, for every 100 units of currency spent, 40 units were gained as profit. The basic formula for profit is:

• Profit = Selling Price - Cost Price

To convert this into a percentage profit, which is often more useful for comparison purposes, you use:

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

The key takeaway here is understanding how any percentage in profit or sales directly affects your final earnings. In the solved exercise, we initially calculate the selling price by taking into account a 40% profit markup on the cost price, which is expressed as \(1.4C\). This method applies to any situation where a profit margin needs to be accounted before determining the selling price.

Discount Calculation

When items are sold at a discount, it means they're being offered at a price lower than the original or marked price. This is often expressed in percentages. Understanding how discounts affect the selling price is crucial for both buyers and sellers.Let's add some insights here:

• A discount can be calculated by subtracting the discount percentage of the selling price from the initial selling price.
• Discount Amount = Initial Selling Price \(\times\) Discount Percentage
• Discounted Price = Initial Selling Price - Discount Amount

In the original problem, there is a 20% discount applied to an item that was initially sold at a 40% profit. With the initial price calculated, the discount price was determined using the formula:

• Discounted Selling Price = Initial Selling Price - (20% of Initial Selling Price)

For instance, starting with an initial selling price expressed as \(1.4C\) (considering a 40% profit), the discounted price results in \(1.12C\). This shows how each percentage directly brings down the initial value, altering the final price significantly.

Selling Price

The selling price of an item is the amount a buyer pays to purchase it. Selling prices aren't always straightforward—they can be influenced by various factors like cost price, desired profit, and discounts. Let’s break down these influences:

• Base Cost: The initial amount spent to acquire or produce the item, denoted here as "C".
• Profit Margin: This is the additional charge added to the cost, to make a profit. For example, a 40% profit means selling at \(1.4C\).
• Discounts: Any reduction offered from the selling price. A discount typically reduces the selling price, encouraging more purchases.

After applying a desired profit (40% in the situation described) and later offering a discount (20%), the ultimate selling price becomes fundamental for calculating actual earnings. Thus, understanding these elements allows for effective pricing strategies and evaluations of deals or sales. In this exercise, the end result was a selling price of \(1.12C\), after considering the costs, profit, and discount.