Calculating Profit or Loss Percentage with Markup and Discount

This question asks us to determine the overall profit or loss percentage when a trader first increases the price of goods (marks up) and then offers a discount on the increased price.

To solve this problem, we can assume a simple value for the Cost Price (CP) and then calculate the Marked Price (MP) and Selling Price (SP) based on the given percentages.

Let's assume the Cost Price (CP) of the goods is ₹100.

Step 1: Calculate the Marked Price (MP)

The trader marks his goods 15 percent above the cost price. This means the markup is 15% of the CP.

Markup Amount $= 15\% \text{ of CP}$

Markup Amount $= \frac{15}{100} \times 100 = ₹15$

The Marked Price (MP) is the Cost Price plus the Markup.

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

MP $= ₹100 + ₹15 = ₹115$

Step 2: Calculate the Discount Amount

The trader offers a 40 percent discount on the Marked Price.

Discount Amount $= 40\% \text{ of MP}$

Discount Amount $= \frac{40}{100} \times 115$

Discount Amount $= \frac{2}{5} \times 115$

Discount Amount $= 2 \times 23 = ₹46$

Step 3: Calculate the Selling Price (SP)

The Selling Price (SP) is the Marked Price minus the Discount Amount.

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

SP $= ₹115 - ₹46 = ₹69$

Step 4: Determine Profit or Loss

Now we compare the Selling Price (SP) with the Cost Price (CP).

CP $= ₹100$

SP $= ₹69$

Since SP < CP, there is a Loss.

Loss $= \text{CP} - \text{SP}$

Loss $= ₹100 - ₹69 = ₹31$

Step 5: Calculate the Loss Percentage

The Loss Percentage is calculated on the Cost Price.

Loss Percentage $= \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100$

Loss Percentage $= \left( \frac{31}{100} \right) \times 100 = 31\%$

Therefore, the trader incurs a 31 percent loss.

Revision Table: Key Concepts in Profit and Loss

Additional Information on Markup and Discount

Markup and discount are common practices in business. Markup increases the potential selling price, while discount attracts customers by reducing the price from the marked price. The final profit or loss depends on the combined effect of the markup percentage and the discount percentage.

In this scenario, a 15% markup followed by a 40% discount resulted in an overall loss. This is because the discount percentage (40%) applied to the higher marked price had a larger impact than the markup percentage (15%) applied to the original cost price.

It's important to note that markup is usually calculated on CP, while discount is always calculated on MP.

Sometimes, problems might involve successive discounts or scenarios where the discount is given as a fixed amount rather than a percentage. The core principle remains calculating the final Selling Price and comparing it with the Cost Price.