Question

Even after a discount of \(q \%\) on marked price a trader gains by \(p \%\) What is the markup percentage over the cost price? (a) \(\frac{p+q}{(q-p)} \times 100\) (b) \(\frac{p+q}{(100-p)} \times 100\) (c) \(\frac{p+q}{(100-q)} \times 100\) (d) not possible

Short answer

Answer: (c) \(\frac{p+q}{(100-q)} \times 100\)

Step-by-step solution

Define the variables

Let's define the variables: - \(M\) is the marked price - \(C\) is the cost price - \(q \%\) is the discount percentage - \(p \%\) is the gain or profit percentage after the discount is applied - \(S\) is the selling price after the discount is applied

Write the equations related to the problem

We know that: 1. Selling price after discount is \(S = M * (1 - \frac{q}{100})\) 2. Profit percentage is calculated as \(p \% = \frac{S - C}{C} * 100\) We are looking for the markup percentage as \(\frac{M - C}{C} * 100\).

Substitute and solve for the markup percentage

From equation 1, we can write \(S\) in terms of \(M\) and \(q \%\): \(S = M * (1 - \frac{q}{100})\) Now, use the equation for profit percentage to substitute \(S-C\) from equation 2: \(p \% = \frac{M * (1 - \frac{q}{100}) - C}{C} * 100\) Rearrange the equation to solve for the markup percentage: \(100 \cdot (p\% + q\%) = \frac{M - C}{C} * 100\) Therefore, the markup percentage is: \(\frac{p+q}{(100-q)} \times 100\) So, the correct option is (c) \(\frac{p+q}{(100-q)} \times 100\).

Key concepts

Discount and Profit Equation

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Markup Calculation

Markup calculation denotes the process of determining the amount by which the cost price of an item is increased to reach its selling price before any discounts. It is the additional percentage added to the cost price to cover expenses and profit.

For markup calculation, you need to find out by how much, percentage-wise, the marked price exceeds the cost price. This is especially useful in determining how much a product can be discounted without incurring a loss. The formula used for markup calculation is represented as \(\frac{M - C}{C} \cdot 100\%\), where \(M\) signifies the marked price and \(C\) the cost price. Simplifying the relationship between discount, profit, and markup can lead to a better understanding of pricing strategies.

Profit Percentage

The profit percentage is a financial metric indicating the level of profitability of a sale. It is the percent gain made on the sale of an item relative to its cost price. To compute profit percentage, use the formula \(p \% = \frac{S - C}{C} \cdot 100\), where \(S\) defines the selling price after any discounts, and \(C\) is the cost price.

Understanding profit percentage is crucial for businesses to set appropriate pricing and discount strategies. It informs businesses how much they're earning relative to the initial investment in their goods. Moreover, knowing this percentage can aid in identifying the price point at which the product breaks even or starts making a profit.

Selling Price After Discount

The selling price after a discount is applied is an important figure for consumers and retailers alike. It's the final amount that a buyer pays for an item after the reduction of a certain percentage from its marked price. Calculating this price involves taking the original marked price and subtracting the marked percentage (discount) from it.

Formula to Calculate Selling Price After Discount:

\(S = M \cdot (1 - \frac{q}{100})\), where \(M\) is the marked price, and \(q\) represents the discount percentage. This formula helps both sellers and buyers to know exactly how much is to be paid post-discount, facilitating financial planning and budgeting.

Markup Calculation

Markup calculation denotes the process of determining the amount by which the cost price of an item is increased to reach its selling price before any discounts. It is the additional percentage added to the cost price to cover expenses and profit.

For markup calculation, you need to find out by how much, percentage-wise, the marked price exceeds the cost price. This is especially useful in determining how much a product can be discounted without incurring a loss. The formula used for markup calculation is represented as \(\frac{M - C}{C} \cdot 100\%\), where \(M\) signifies the marked price and \(C\) the cost price. Simplifying the relationship between discount, profit, and markup can lead to a better understanding of pricing strategies.

Profit Percentage

The profit percentage is a financial metric indicating the level of profitability of a sale. It is the percent gain made on the sale of an item relative to its cost price. To compute profit percentage, use the formula \(p \% = \frac{S - C}{C} \cdot 100\), where \(S\) defines the selling price after any discounts, and \(C\) is the cost price.

Understanding profit percentage is crucial for businesses to set appropriate pricing and discount strategies. It informs businesses how much they're earning relative to the initial investment in their goods. Moreover, knowing this percentage can aid in identifying the price point at which the product breaks even or starts making a profit.

Selling Price After Discount

The selling price after a discount is applied is an important figure for consumers and retailers alike. It's the final amount that a buyer pays for an item after the reduction of a certain percentage from its marked price. Calculating this price involves taking the original marked price and subtracting the marked percentage (discount) from it.

Formula to Calculate Selling Price After Discount:

\(S = M \cdot (1 - \frac{q}{100})\), where \(M\) is the marked price, and \(q\) represents the discount percentage. This formula helps both sellers and buyers to know exactly how much is to be paid post-discount, facilitating financial planning and budgeting.