CAT 2025 Lesson : Profit & Loss - Marked Price

4. Marked Price and Discount

Going forward, CP, SP and MP represent Cost Price, Selling Price and Marked Price respectively.

For some products, such as clothing and electronics, discounts or discount sales are a norm. This means the sellers offer a discount over the stated price to arrive at the actual selling price. This stated price is called Marked Price (MP) . This is the price of a product stated by the seller before any discount.

List Price (LP) is a price determined by the manufacturer, and typically marked on the product, as the price at which retailers have to sell the products. Maximum Retail Price or MRP stated in the packages of fast moving consumer goods, such as soaps, detergents, beverages, etc. are examples of List Prices. These are printed on the packages by the manufacturer. In entrance tests, however, List Price and Marked Price are used interchangeably. So, whatever applies for MP, applies for LP as well.

Let's understand the concept of Marked Price and Discount with the following example.

A trader buys pens at Rs. $\bm{100}$ per pen, which is the CP. To make it attractive for customers, she wants to offer a discount.

Therefore, she first marks up the price by $\bm{50\%}$. At this moment, only the CP is known to the trader. Therefore, the mark-up $\%$ is applied on the CP.

Marked Price (MP) $=$ CP + 50 $\%$ of CP $= 100 + 50 =$ Rs. $150$

This MP of Rs. $150$ per pen is displayed as the price to customers. The trader then offers a discount of $\bm{20\%}$. The trader cannot and will not inform her CP to the customer. Therefore, the discount $\%$ will be applied on the MP, which the customer is aware of. This discount when subtracted from the MP, will give the Selling Price (SP), which is the value for which the pen is actually sold.

Selling Price (SP) $=$ MP $- 20 \%$ of MP $= 150 - 30 =$ Rs. $120$

To summarise, the two legs in Marked Price & Discount are as follows.
1) MP = CP + Mark-up Value
⇒ MP $=$ CP + Mark-up $\%$ of CP
⇒MP $=$ CP ($\bm{1}$ + Mark-up %) $\longrightarrow$ ($1$)

2) SP = MP - Discount
⇒ SP $=$ MP - Discount $\%$ of MP
⇒ SP = MP ($\bm{1}$ – Discount %) $\longrightarrow$ ($2$)

3) Substituting equation ($1$) in ($2$), we get
SP = CP ($\bm{1}$ + Mark up %) ($\bm{1}$ - Discount %)

Also note the following.
1) Profit/Loss % is a percentage of CP.
2) Mark-up % is a percentage of CP.
3) Discount % is a percentage of MP.