Topics to be learn : Discount Commission Rebate

Recall :

A percent (or per cent) is a way of expressing a number as a fraction of 100.

The term "per cent" is represented by the symbol %.

For example, 12 per cent is written as 12% and is mathematically equivalent to the fraction \(\frac{12}{100}\).

Any percentage can be written as a fraction with a denominator of 100, such as 47% = \(\frac{47}{100}\) or 86% = \(\frac{86}{100}\).

To find a specific percentage of a total, multiply the total by the percentage fraction.

Examples:

(i) To find 4% of 300, calculate 300 × \(\frac{4}{100}\), which equals 12.

(ii) To find 15% of 1700, calculate 1700 × \(\frac{15}{100}\), which equals 255.

In business transactions, percentages are the standard way to express

• discounts (given on the marked price),
• commissions (paid to agents based on the selling price), and
• rebates (incentives often backed by the government).

Discount :

A discount is a reduction in the price of an item, which is typically offered by a shopkeeper to attract customers.

To calculate values related to discounts, the following mathematical relationships are used:

Discount = Marked Price – Selling Price.

Selling Price = Marked Price – Discount.

Percentage of Discount: If the discount percentage is x, it can be expressed as: \(\frac{x}{100}\) = \(\frac{Discount}{Marked\,Price}\).

∴ Discount = Marked Price × \(\frac{x}{100}\)

• Marked Price (M.P.): This is the price printed on the item's tag or label. It is also referred to as the printed price.
• Selling Price (S.P.): This is the actual price a customer pays after the discount has been subtracted from the marked price.

Calculating a Discount :

Discounts are almost always expressed as a percentage of the marked price.

Example:

If a book has a marked price of ₹ 75 and is sold at a 12% discount, the discount amount is calculated as:

∴ Discount = 75 × \(\frac{12}{100}\) = ₹ 9.

∴ Selling Price = Marked Price – Discount = ₹ 75 - ₹ 9 = ₹ 66.

The Monsoon Saree Sale (Strategy of Discount) :

Using data from Mr. Suresh’s Saree Shop, we can see that a discount isn't just a gift to the customer—it’s a calculated business move.

Month	Profit per Saree	Number of Sarees Sold	Total Monthly Profit
June (No Discount)	Rs. 50	40	Rs. 2,000
July (Monsoon Discount)	Rs. 30	100	Rs. 3,000

Strategy:

Mr. Suresh made Rs. 20 less per saree in July, but his bank account grew by Rs. 1,000 more than in June. Why?

• Selling a high number of items at a lower profit (Volume) often results in more money than selling a few items at a high profit (Margin).
• Items sitting on a shelf are "frozen" money. By clearing out stock during a Monsoon Sale, Mr. Suresh frees up space for new winter styles.
• A business needs cash moving through it constantly to pay bills and buy new stock. Selling 100 sarees quickly provides the "Cash Flow" needed to keep the business healthy.

Solved Examples :

(1) The marked price of a book is Rs. 360. The shop keeper sold it for Rs. 306. How much percent discount did the shopkeeper give ?

Solution:

Marked Price = ₹ 360, Selling Price = ₹ 306.

∴ Discount = 360 - 306 = ₹ 54.

On marked price of Rs. 360, the discount is 54 rupees.

∴ if the marked price is ₹ 100, let the discount be x.

\(\frac{Discount}{Marked\,Price}\) = \(\frac{x}{100}\)

∴ \(\frac{54}{360}\) = \(\frac{x}{100}\)

∴ x = \(\frac{54}{360}\ × 100 = 15

∴ 15% discount is given on the book.

(2) After giving a discount of 20%, a saree is sold for Rs. 1120. Find the marked price of the saree.

Solution :

Let us assume that the actual marked price of the saree, which was sold for Rs. 1120, was x.

Discount = Marked Price × Discount Percent = x × \(\frac{20}{100}\) = 0.2x

Selling Price = Marked Price – Discount

∴ 1120 = x – 0.2x

1120 = 0.8x

∴ x = \(\frac{1120}{0.8}\) = 1400

∴ Marked Price (x) = Rs. 1400

 Commission :

When a company or individual cannot sell goods or property directly, they employ a commission agent. The remuneration paid to this individual for their service is known as Commission.

• The Difference (Discount & Commission) : A discount is a price cut for the buyer. A commission is a fee paid to a third party for their expertise and help.

The Role of the Agent :

• Mediators: Agents often act as mediators between buyers and sellers for high-value assets such as land, houses, and cattle.
• Market Facilitators: In agricultural markets, agents facilitate the sale of foodgrains, vegetables, fruits, and flowers.
• Payment Structure: Commission is calculated as a percentage of the transaction value. Depending on the agreement, it may be received from the seller, the buyer, or both.

Brokerage in Real Estate : In property transactions, the commission is often referred to as brokerage.

Note : Commission is a percentage of the total transaction value. It is either subtracted from the seller's final check or added as an extra cost for the buyer.

Examples :

(1) The Shripati Land Sale (Brokerage) :

Shripati sold land for Rs. 2,50,000 through a Broker. Because the broker provided a service to both the seller (finding a buyer) and the buyer (finding the land), he charged a 2% fee to both sides.

Brokerage from one side = 2,50,000 × \(\frac{2}{100}\) = Rs. 5,000

Total Remuneration = Rs. 5,000 (from Seller) + Rs. 5,000 (from Buyer) = Rs. 10,000 total.

(2) The Sukhdeo Wheat Sale (Agent) :

Sukhdeo sold 10 quintals of wheat at Rs. 4,050 per quintal through an Agent at a 1% commission rate.

Total Sale Value = 10 × 4,050 = Rs. 40,500

Commission Deduction: 40,500 × \(\frac{1}{100}\) = Rs. 405

Sukhdeo receives 40,500 - 405 = Rs. 40,095.

Rebate :

A rebate is a specific type of discount granted under certain conditions by the government or recognized institutions (e.g., Khadi Gramodyog Bhandar, Handloom shops, Handicraft Emporiums).

Characteristics of Rebates :

• Compensation: Unlike a standard retail discount where the shopkeeper bears the cost, the amount of a rebate is compensated by the government.
• Forms of Rebate: It can be a lump sum or a percentage of the printed price.
• Income Tax Rebate: Individuals with income below a certain limit receive a discount on their payable income tax, which is also formally termed a rebate.

Which Principle Applies?

Principle	Typical Context	Who Benefits	Who Pays/Compensates
Discount	Retail Sales (e.g., Monsoon Sale)	The Buyer	The Shopkeeper (accepts lower profit)
Commission	Property or Agricultural Sales	The Agent/Broker	The Seller and/or the Buyer
Rebate	Khadi/Handloom Sales	The Buyer	The Government (repays the shop)