The principles of profit and loss can be very useful in real-life situations. A product always has a cost price and a selling price, and profit or loss can be calculated by calculating the difference between the cost price and the selling price of a product. Nearly all business models keep this principle as the focal point of their operation, as evaluating profit and loss helps to assess the ongoing situation and the profitability of a business.

This topic is an integral part of the quantitative section of various competitive exams like GMAT, GRE, CAT, etc. It’s a blend of similar concepts that are very easy to understand. The difficulty level of questions fluctuates depending on the nature of the exams. 

In this article, we will provide a clear understanding of the concepts of this topic.

Basic Terms of Profit and Loss

The very first thing you must do to get a hang of this topic is understand its basic terminology and concepts. These are the important terms related to the topic of profit and loss: 

  • Cost Price (CP): The amount at which a vendor purchases a product. It can include various auxiliary costs like overhead expenses, transportation costs, etc. For example, you bought an almirah at Rs 25,000 and spent Rs 2,500 for transportation and Rs 500 for set up. Hence, the total cost price is the sum of all the expenditures made, which amounts to Rs 28000. 
  • Selling Price (SP): The amount at which a vendor sells a product. It can be more than, equal to or less than the cost price of the product. For example, if a trader buys a bike for Rs. 50,000 and sells it for Rs. 70,000, then the bike’s cost price is 50,000 and its selling price is 70,000.
  • Profit  (P): If a product is sold at a price greater than its cost price then the seller makes a profit. For example, if a plot is purchased for Rs 50,000 and sold for Rs 1,50,000 three years later, there is a profit of Rs 1 lakh.
  • Profit Percentage (P%): The percentage of profit made by a vendor by selling a product at a price greater than its cost price is called profit margin or profit percentage.
  • Loss (L): If a product is sold at a price lesser than its cost price then the vendor incurs a loss. For example, Ravi purchased a cell phone for Rs 7,000 and sold it for Rs 5,000 six months later, incurring a loss of Rs 2,000.
  • Loss Percentage (L%): The percentage of loss incurred by a vendor by selling a product at a price lesser than its cost price is called loss percentage.
  • Marked Price (MP): The price that the shopkeeper places on a product to provide a discount is called the marked price.
  • Discount:  A reduction in the price of a product offered by a vendor to customers. It is calculated by subtracting the selling price from the marked price.
  • Discount Percentage (D%): The percentage of discount given to a customer by a shopkeeper over the marked price is called the discount percentage.
  • Percentage Increase and Decrease: The percentage of increment or reduction on the base value of any product or its profit/loss.

Concept Driven Formulas

Profit (SP>CP)Loss (CP>SP)
1. Profit = Selling Price – Cost Price

2. Selling Price = Cost Price + Profit

3. Cost Price = Selling price – Profit

4. Profit% = Profit X \frac{100}{Cost Price}

5. Cost Price = \left{ \frac{100}{100+Profit%}\right} X Sales Price
(When Sales Price > Cost Price)

6. Profit = Profit X \frac{Cost Price}{100}
1. Loss = Cost Price –  Selling Price

2. Cost Price = Selling Price + Loss

3. Selling Price = Cost Price – Loss

4. Loss% = Loss X \frac{100}{Cost Price}

5. Cost Price = \left{\frac{100}{100-Loss%} \right}\times Sales Price (When Sales Price < Cost Price)

6. Sales Price = \left{\frac{100+Profit%}{100} \right}\times Cost Price (When Sales Price > Cost Price)
  • Discount = Marked Price – Selling Price

  • Discount Percentage = \frac{Discount}{Marked Price} x 100

  • Increase% = Increment X \frac{100}{Original Value}

  • Decrease% =  Reduction X \frac{100}{Original Value}

Sample Questions

  1. The price of an article is increased by 25%, by how much percent, must the new price of this article be decreased to restore its original price?
  1. 10%
  2. 20%
  3. 21%
  4. 24%
  5. 25%

Answer: B

Explanation: 

Let the initial of the article be Rs. 100.

Given,

It increased by 25%

So, the new price will be 125.

Question:

By how much percent, must the new price of this article be decreased to restore its original price?

Percent change =\frac{Difference of initial and final value}{Initial value} * 100

Key:

Initial value = Least Value among the two values if question asks for increase or more

Initial value = Highest Value among the two values if question asks for decrease or less

So, in our question,

Percent change = \frac{Difference of initial and final value}{Initial value} * 100

 = ((125-100)/ 125) *100

= (25/ 125) * 100

= 20% 

Hence the answer is B.

  1. The original price of a painting is reduced by 25%. During a special sale, the new price was reduced by 10 per cent. By approximately what percent would the price now have to be increased in order to restore the price of the painting to its original amount?
  1. 32.5
  2. 35
  3. 48
  4. 65
  5. 67.5

Answer: C

Explanation: 

We know that,

Overall % change = a+b+ \frac{ab}{100}

Where “a” and “b” successive changes,

In our question,

Both “a = -25” and “b = -10”

So, 

Overall % change = -25-10+ \frac{250}{100} = -35 + 2.5 = -32.5

Price will decrease by 32.5%

So, the new decreased price will be 100 – 32.5 = 67.5

Question:

By approximately what percent would the price now have to be increased in order to restore the price of the painting to its original amount?

Percent change = \frac{Difference of initial and final value}{Initial value} * 100

Key:

Initial value = Least Value among the two values if question asks for increase or more

Initial value = Highest Value among the two values if question asks for decrease or less

So, in our question,

Percent change = \frac{Difference of initial and final value}{Initial value} * 100

 = ((100-67.5)/ 67.5) *100

= (32.5/ 67.5) * 100= 48.14 ~ 48. Hence the answer is C.

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