Understanding the Profit and Loss Scenario

This problem involves concepts of cost price, marked price, selling price, markup percentage, profit percentage, and discount percentage. A merchant first increases the price of an article (markup) and then reduces it (discount) to arrive at the selling price, making a profit in the process.

Calculating Marked Price (MP)

The merchant marks the price 20 percent above the cost price (CP). Let's assume the Cost Price is $\text{CP}$.

The markup percentage is 20%.

Marked Price (MP) is calculated as:

$\text{MP} = \text{CP} + \text{Markup Amount}$

$\text{Markup Amount} = \text{CP} \times \frac{20}{100} = 0.20 \times \text{CP}$

So, $\text{MP} = \text{CP} + 0.20 \times \text{CP} = 1.20 \times \text{CP}$

Calculating Selling Price (SP)

The merchant earns a profit of 10 percent on the Cost Price. The profit percentage is 10%.

Selling Price (SP) is calculated as:

$\text{SP} = \text{CP} + \text{Profit Amount}$

$\text{Profit Amount} = \text{CP} \times \frac{10}{100} = 0.10 \times \text{CP}$

So, $\text{SP} = \text{CP} + 0.10 \times \text{CP} = 1.10 \times \text{CP}$

Determining the Discount Amount

The discount is given on the Marked Price (MP) to arrive at the Selling Price (SP).

Discount Amount = Marked Price - Selling Price

Discount Amount = $\text{MP} - \text{SP}$

Substitute the values we found for MP and SP in terms of CP:

Discount Amount = $1.20 \times \text{CP} - 1.10 \times \text{CP}$

Discount Amount = $(1.20 - 1.10) \times \text{CP} = 0.10 \times \text{CP}$

Calculating the Discount Percentage

The discount percentage is calculated on the Marked Price (MP).

Discount Percentage = $\frac{\text{Discount Amount}}{\text{Marked Price}} \times 100$

Substitute the values for Discount Amount and Marked Price:

Discount Percentage = $\frac{0.10 \times \text{CP}}{1.20 \times \text{CP}} \times 100$

The 'CP' terms cancel out:

Discount Percentage = $\frac{0.10}{1.20} \times 100$

Discount Percentage = $\frac{1}{12} \times 100$

Discount Percentage = $\frac{100}{12}$

Now, we calculate the value:

$\frac{100}{12} = \frac{50}{6} = \frac{25}{3}$

As a decimal, $\frac{25}{3} \approx 8.333...$

So, the discount percentage is approximately 8.33 percent.

Step-by-Step Calculation Summary

1. Assume Cost Price (CP).
2. Calculate Marked Price (MP) using the 20% markup on CP. MP = 1.20 * CP.
3. Calculate Selling Price (SP) using the 10% profit on CP. SP = 1.10 * CP.
4. Calculate Discount Amount = MP - SP = 1.20*CP - 1.10*CP = 0.10*CP.
5. Calculate Discount Percentage = (Discount Amount / MP) * 100.
6. Substitute values: ((0.10*CP) / (1.20*CP)) * 100 = (0.10 / 1.20) * 100.
7. Simplify the fraction: (1/12) * 100 = 100/12.
8. Calculate the final percentage: 100/12 ≈ 8.33%.

Revision Table: Key Formulas

Additional Information on Profit, Loss, and Discount

In business, understanding the relationship between cost price, marked price, selling price, profit, and discount is crucial. Here's a bit more detail:

• Cost Price (CP): This is the original price at which an article is bought or manufactured.
• Marked Price (MP): This is the price displayed on the article. It is often higher than the cost price, allowing room for discounts or negotiations. It is also known as the list price.
• Selling Price (SP): This is the price at which the article is actually sold to the customer.
• Profit: Occurs when SP > CP. Profit = SP - CP.
• Loss: Occurs when SP < CP. Loss = CP - SP.
• Markup: The amount added to the cost price to get the marked price. Markup = MP - CP. Markup percentage is usually calculated on CP.
• Discount: The reduction offered on the marked price. Discount = MP - SP. Discount percentage is always calculated on MP.

The discount percentage calculation specifically uses the marked price as the base, not the cost price or selling price. This is a common point of confusion, so it's important to remember which price is used as the denominator for each percentage calculation (profit/loss on CP, discount on MP, markup on CP).