#### Introduction

In the Quantitative Section of the CLAT, the numerical ability of the candidate is tested. The questions are based upon the basic concepts of elementary mathematics that we study upto Class 10^{th}. The questions are usually from Arithmetic and Algebra and not from the Calculus portion. This Article is a quick revision of Profit and Loss for CLAT.

Although the pattern of CLAT examination for 2020 was changed by the Consortium of NLUs and all the questions including mathematical ability were in the form of passages, it is still important to understand all the concepts separately in order to accurately and quickly solve those passage based questions. In this article, we will be explaining the basic terms related to the chapter of Profit Loss and discount along with the Formulas and Questions for Practice.

#### Important Definitions

- Cost Price: The price at which a certain good is bought is referred to as the cost price.
- Selling Price: The Price at which a certain good is sold off is called as the Selling Price.
- Marked Price: It is different from both selling price and the cost Price. It is the price marked on the good and discount is offered on this price.
- Discount: The Concession offered on a product on the marked price is called as the Discount.
- Profit: The difference between selling Price and Cost Price when Selling Price is greater than the cost price, is called as Profit. While calculating the profit percentage, it is done relative to the cost price.

- Loss: The difference between selling Price and Cost Price when Cost Price is greater than the Selling price, is called as Loss. While calculating the Loss percentage, it is done relative to the cost price.

#### Important Formula

- Selling Price = Cost Price (+/ -) Profit/Loss
- Discount = Marked Price – Selling Price
- Discount Percentage = (Discount/Marked Price) *100
- Profit = Selling Price – Cost Price
- Loss = Cost Price – Selling Price
- Profit Percentage = (profit/Cost Price) *100
- Loss Percentage = (Loss/ Cost Price) *100
- Selling Price = [(100 + P%)/100] * CP
- Cost Price = [100/ (100+P%)] *SP
- If the loss is l% and the profit is p%, then the net profit/loss = (p-l- pl)/100

#### Illustrations

- Geeta mixed 7 dozen of Bananas priced at Rs. 60/ dozen with 8 dozen of banana priced at Rs. 40/dozen. Find the profit / loss percentage if the mixture is sold at Rs. 50 per dozen.

Solution: Total cost price for the mixture = (7*60) + (8* 40) = 420 + 320

= Rs. 740

Total Selling Price of the Mixture = 15 *50 = 750

Since Selling Price > Cost Price, therefore it is a profit.

Profit Percentage = (10/ 740) *100 = 1.3%

- If the product is marked at Rs. 100 and sold at Rs. 80, find the discount percentage?

Solution: Discount = Marked Price – Selling Price = 100 – 80 = 20

Discount Percentage = (20/100) *100 = 20 %

- If a mug costs Rs. 200 after 20% discount, calculate the marked price of the pen?

Solution: Using the formula

Marked Price – Selling Price = Discount ; and

Marked Price (100 – 20)/100 = 200

Marked Price (80/100) = 200

Marked Price = (200*100)/80

= Rs. 250