Mastering Profit and Loss: Formulas, Concepts, and Solved Problems

Profit and Loss Formula: In mathematics, the profit and loss concept is essential for evaluating market trends and determining the financial viability of a business. Every product carries a cost price (C.P.) and a selling price (S.P.). By comparing these, you can calculate the profit earned or loss incurred on any commodity. Simply put, when the selling price exceeds the cost price, the business generates a profit; if the purchase price is higher than the selling price, it results in a loss. This article covers the fundamental principles of profit and loss, key formulas, and practical solved examples to sharpen your skills.

Profit and Loss Basic Concepts

Understanding profit and loss is a vital life skill, as these transactions define everyday commerce. Mastering this concept allows you to navigate various economic scenarios efficiently. There are various terms used to deal with the profit and loss concepts like the cost price of the product (C.P.), the selling price of the product (S.P.), discount on the product, marked price of the product, profit, and loss. Let's break down these essential components in detail.

Cost Price

The cost price refers to the amount at which an item is bought in the market. For instance, if you purchase a pen for Rs. 15, the cost price of that item is Rs. 15. In mathematical terms, this is expressed as C.P.

Selling Price

The selling price refers to the amount at which an item is sold in the market. If you sell that same pen for Rs. 20, the selling price is Rs. 20. This is typically expressed as S.P.

Profit

Within a transaction, if the selling price of a product is more than the cost price of that particular product, then it denotes the profit. For example, by selling a pen bought at Rs. 15 for Rs. 20, you earn a profit of Rs. 5. This can be calculated using the following basic formula. 

Profit = Selling price - Cost price

Using our previous example, where the cost price was Rs. 15 and the selling price was Rs. 20: Profit = 20 - 15 = Rs. 5.

Loss

Conversely, if the selling price of a product is lesser than the cost price of that particular product, then it denotes the loss. For example, if a book is purchased for Rs. 100 but sold for only Rs. 80, the transaction results in a loss of Rs. 20. This is determined by the formula below. 

Loss = Cost price - Selling price

In the book example, the cost price is Rs. 100 and the selling price is Rs. 80. Therefore, the Loss = 100 - 80 = Rs. 20.

Marked Price

The marked price refers to the price fixed by the seller by putting a label on the product. It serves as the base price at which the seller provides a discount in the market. Once a discount is applied to the marked price, the item is sold at the final selling price. For example, if a store offers a 50% discount on an item marked Rs. 130, then the Marked Price is Rs. 130.

Discount

A discount is a rebate or the offer provided by the shopkeepers or businessmen to attract customers to their products. Discounts are used to boost sales and manage market competition, and are always given on the Marked price of the product. The standard discount formulas are provided below.

Discount = Marked Price - Selling Price

Discount (%) = (Discount / Marked Price) × 100

If an item with a marked price of Rs. 260 has a 20% discount offer, the selling price can be calculated as follows:

20% discount on marked price = (20/100) × 260

Discount offered = Rs. 52

Hence, Selling Price = Marked Price - Discount 

Selling Price = 260 − 52 = 208

Profit and Loss Formula

When the selling price and cost price are known, use these formulas to calculate profit or loss. The profit formula is used when the selling price of an item is higher than the cost price of that item. It is outlined below. 

Profit = Selling price (S.P.) - Cost price (C.P.)

The loss formula is used when the cost price of an item is higher than the selling price of that item. It is outlined below. 

Loss = Cost price (C.P.) - Selling price (S.P.)

Often, you will need to express profit or loss as a percentage. The percentage of profit and loss provides a clearer view of the profit or loss relative to the cost, which is essential for comparing different business scenarios. The formulas for profit and loss percentages are mentioned below.

1. Profit percentage (P%) = (Profit / Cost Price) × 100

2. Loss percentage (L%) = (Loss / Cost price) × 100

3. S.P. = {(100 + P%) / 100} × CP (if SP > CP)

4. S.P. = {(100 – L%) / 100} × CP (if SP < CP)

5. C.P. = {100 / (100 + P%)} × SP (if SP > CP)

6. C.P. = {100 / (100 – L%)} × SP (if SP < CP)

Profit and Loss Formula Solved Examples 

Question 1: If a person purchases 2 kg of grapes for Rs. 160 and sells them for Rs. 90 per kg, what is the total profit?

Solution: The cost price (CP) for 2 kg of grapes is Rs. 160.

The selling price (SP) per kg is Rs. 90.

Total SP for 2 kg of grapes = 90 x 2 = Rs. 180.

Since SP > CP, the profit is: P = SP – CP

Profit (P) = 180 – 160 = Rs. 20.

Question 2: Suppose a lady buys 1 kg of bananas for Rs. 80 and sells them for Rs. 70 per kg. Is this a profit or loss, and by how much?

Solution: The cost price (CP) for 1 kg of bananas is Rs. 80.

The selling price (SP) for the bananas is Rs. 70.

Since the SP is lower than the CP, the transaction results in a loss.

The loss incurred is: L = CP – SP

Loss (L) = 80 – 70 = Rs. 10.

Question 3: A man buys newspapers at Rs. 12 each and sells them for Rs. 15 each. Calculate his total profit and the profit percentage.

Solution: The cost price (CP) per newspaper is Rs. 12.

The selling price (SP) per newspaper is Rs. 15.

Since the SP is higher than the CP, the man has earned a profit.

Profit = SP – CP

Profit = 15 – 12 = Rs. 3.

Profit percentage (P%) = (Profit / Cost Price) × 100

Profit percentage = (3 / 12) × 100 = 25%.

Question 4: Sneha sells a mobile phone for Rs. 15,500, incurring a 4% loss. What was the original cost price of the phone?

Solution: The selling price (SP) is Rs. 15,500.

The loss percentage (L%) is 4%.

A 4% loss implies that for a cost of Rs. 100, the loss is Rs. 4.

Let the C.P. be Rs. 100.

S.P. = C.P. - Loss = 100 - 4 = Rs. 96.

If S.P. is Rs. 96, then C.P. is Rs. 100.

For an S.P. of Rs. 15,500, C.P. = (100 / 96) × 15,500 ≈ Rs. 16,145.83.

Question 5: If the cost price of 9 pencils is equal to the selling price of 6 pencils, calculate the profit percentage.

Solution: Given, CP of 9 pencils = SP of 6 pencils.

Assume the cost price of one pencil is x.

CP of 9 pencils = 9x.

SP of 6 pencils = 9x.

CP of 6 pencils = 6x.

Applying the profit formula:

Profit = SP - CP

Profit = 9x - 6x = 3x.

Profit % = (Profit / CP of 6 pencils) × 100

Profit % = (3x / 6x) × 100 = 50%.