Understanding Profit and Loss Percentage with Markup and Discount

This question asks us to determine the final profit or loss percentage when an article's price is first increased (marked up) above the cost price and then a discount is offered on this new marked price.

To solve this, we need to follow these steps:

1. Assume a suitable value for the Cost Price (CP).
2. Calculate the Marked Price (MP) based on the given markup percentage.
3. Calculate the Selling Price (SP) based on the given discount percentage on the Marked Price.
4. Compare the Selling Price (SP) with the Cost Price (CP) to find the profit or loss amount.
5. Calculate the profit or loss percentage.

Step 1: Assume Cost Price (CP)

Let's assume the Cost Price (CP) of the article is ₹100. Choosing 100 makes percentage calculations very easy.

$\text{CP} = ₹100$

Step 2: Calculate Marked Price (MP)

The article is marked 36% above the Cost Price.

Markup percentage = 36%

$\text{Marked Price (MP)} = \text{CP} + \text{Markup Percentage of CP}$

$\text{MP} = ₹100 + 36\% \text{ of } ₹100$

$\text{MP} = ₹100 + \left(\frac{36}{100} \times 100\right)$

$\text{MP} = ₹100 + ₹36$

$\text{MP} = ₹136$

So, the Marked Price is ₹136.

Step 3: Calculate Selling Price (SP)

A discount of 30% is offered on the Marked Price.

Discount percentage = 30%

$\text{Selling Price (SP)} = \text{MP} - \text{Discount Percentage of MP}$

$\text{SP} = ₹136 - 30\% \text{ of } ₹136$

$\text{SP} = ₹136 - \left(\frac{30}{100} \times 136\right)$

$\text{SP} = ₹136 - \left(0.3 \times 136\right)$

$\text{SP} = ₹136 - ₹40.8$

$\text{SP} = ₹95.2$

The Selling Price of the article is ₹95.2.

Step 4: Determine Loss or Gain Amount

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

$\text{CP} = ₹100$

$\text{SP} = ₹95.2$

Since the Selling Price (₹95.2) is less than the Cost Price (₹100), there is a Loss.

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

$\text{Loss Amount} = ₹100 - ₹95.2$

$\text{Loss Amount} = ₹4.8$

The loss incurred is ₹4.8.

Step 5: Calculate Loss Percentage

The loss percentage is calculated on the Cost Price.

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

$\text{Loss Percentage} = \left(\frac{₹4.8}{₹100}\right) \times 100$

$\text{Loss Percentage} = 0.048 \times 100$

$\text{Loss Percentage} = 4.8\%$

The final result is a Loss of 4.8%.

Summary of Calculations

Revision Table: Key Terms

Additional Information: Relating Markup, Discount, and Profit/Loss

When a markup and a subsequent discount are applied, the final selling price determines the overall profit or loss relative to the original cost price. It's important to note that the discount is always calculated on the marked price, not the cost price.

There is also a direct formula that relates markup, discount, and overall gain/loss percentage, but the step-by-step method using an assumed CP (like ₹100) is often easier to understand and less prone to errors for many students.

Let M be the markup percentage and D be the discount percentage. The overall gain or loss percentage can be calculated using the formula:

Overall Percentage Change $= \left(M - D - \frac{M \times D}{100}\right)\%$

If the result is positive, it's a gain; if negative, it's a loss.

Using the values from the question: M = 36%, D = 30%

Overall Percentage Change $= \left(36 - 30 - \frac{36 \times 30}{100}\right)\%$

Overall Percentage Change $= \left(6 - \frac{1080}{100}\right)\%$

Overall Percentage Change $= \left(6 - 10.8\right)\%$

Overall Percentage Change $= -4.8\%$

The negative sign indicates a loss. So, there is a Loss of 4.8%. This formula confirms the step-by-step calculation.