# Discount Rate Equation

Discount equations in real life:

In real life , as we see our daily newspapers, banners, advertisements we could see many advertisement that says Buy one take one free, Buy three get four free and sale upto 30 % off.

These are all steps taken by the shopkeepers to fascinate customers to buy more things so that they could clear their old stock and push their sales high. They also announce offer on certain percent on the market price , pretending that they are trying to sell the article in a very low price.
Learning Terms Related to Discount Equations

Marked Price: It is the price of the article which is marked on the article which we are getting. It is denoted as M.P.

Discount: The amount which are deducted by the shop keeper from the marked price is called as discount.

Net price or Selling price: The Amount that we are paying to the shop keeper after discount is called as net price or selling price of the article.

Note: Always the discount is done on the marked price of the article.

Successive Discounts: There is a situation where the shopkeeper advertises two or more discounts one after the other.They are called as successive discounts.
Important Discount Equations:

The important results that are related  to discount are :

Selling price = Marked price - Discount

Discount = M.P. - S.P.

Discount % = `(Discount)/(M.P.)` x 100

M.P. = `(100 X S.P. )/(100 - Discount %)`
Problems Using Discount Equations:

Example 1:The price of a cotton skirt was reduced from \$ 1840 to \$ 1380 by the seller, in summer season. Find the rate of discount offered by the shop keeper

Marked price of the skirt = \$1840

Discount offered on skirt = \$ (1840 - 1380) = \$ 460

Discount % = `(460)/(1840)`

Discount offered = 25 %

Which discount series is better?
10 %, 20 % and 5 %
20 %, 10 % and 5 5

Solution:

Let themarked price of the article be \$ 1000

Solution No.1

Price of the article after the first discount = \$( 1000 x (90/100) = \$ 900

Price of the article after the second discount = \$( 900 x 80/100) = \$720

Price of the article after the third discount = \$(720 x 95/100) = \$ 684

Solution No.2

Price of the article after the first discount = \$( 1000 x (80/100) = \$ 800

Price of the article after the second discount = \$( 800 x 90/100) = \$720

Price of the article after the third discount = \$(720 x 95/100) = \$ 684

The two discount series have the same effect.

Example 2:

Marked price of a book is `\$` 30. It is sold at a discount of 15 %. Find the discount allowed on the book and its selling price.

Solution:

Marked price of the book = `\$` 30

Rate of discount = 15 %

Therefore, Discount allowed = 15 % of `\$` 30

= (15 / 100) × `\$` 30 = `\$` 4.50

Therefore, Selling price of the book = `\$` 30 – `\$` 4.50 = `\$` 25.50.

Example 3:

A table with marked price `\$` 1200 was sold to a customer for `\$` 1100. Find the rate of discount allowed on the table.

Solution:

Marked price = `\$` 1200

Selling price = `\$` 1100

Therefore, Discount = `\$` 1200 – `\$` 1100 = `\$` 100

Rate of discount = (Discount / Marked price) × 100 %

= (100 / 1200)*100% = 8 1/3 %