## Discount

Discount is price reduction given on marked price of an article. It is given by the sellers to increase their sales by attracting customers.
Discount is always calculated with respect to marked price

 Discount = Marked price - Selling price

 Marked price = selling price + Discount

 Selling price = Marked price - Discount

Example: The marked price of a clock is ₹ 3200 and selling price is ₹ 2500. Find the discount price on the clock.
Solution: given, marked price = ₹ 3200
selling price = ₹ 2500
Discount = Marked price - Selling price
= 3200 - 2500
= 700 ₹

 Discount % = Discount × 100 Marked Price

Example: The marked price of a bicycle is ₹ 2500 and selling price is ₹ 1500. Find the discount % on the bicycle.
Solution: given, marked price = ₹ 2500
selling price = ₹ 1500
Discount = Marked price - Selling price
= 2500 - 1500
= ₹1000

 Discount % = Discount × 100 Marked price
 = 1000 × 100 = 40 % 2500

### Successive Discount

A series of discounts are allowed on marked price of an article one after the other, then these discount are called successive discount.
Let x1%,  x2%, x3%……….. be the series of discounts on an article with marked price of ₹ M, then the selling price of the article after all the discount is given by

 Selling Price = M 1 - x1 × 1 - x2 × 1 - x3 100 100 100

Example: A shopkeeper on the eve of Diwali allowed a series of discount on television sets. Find the selling price of a television set, if the marked price of television is ₹ 5000 and successive discount are 20 %, 10 % and 5 %.
Solution: given, marked price = 5000
x1 = 20 %
x2 = 10 %
x3 = 5 %

 Selling Price = M 1 - x1 × 1 - x2 × 1 - x3 100 100 100
 = 5000 1 - 20 × 1 - 10 × 1 - 5 100 100 100
 = 5000 1 - 1 × 1 - 1 × 1 - 1 5 10 20
 = 5000 × 4 × 9 × 19 = 5 × 4 × 9 × 19 5 10 20

= 20 × 171
= ₹ 3420

### Some Useful Shortcut Method

Trick 1: Single discount equivalent to two successive discounts x1% and x2%

 Single Equivalent discount = x 1 + x2 - x1 × x2 % 100

Example: What will be the single equivalent discount for successive discount of 20 % and 10 %.
Solution : given x1 = 10 %
x2 = 20 %

 Single Equivalent discount = x 1 + x2 - x1 × x2 % 100
 = 20 + 10 - 20 × 10 % 100

= 30 - 2
= 28 %

Example: What will be the single equivalent discount for successive discount of 20 % and 20 %.
Solution: given x1 = 20 % & x2 = 20 %.

 Single Equivalent discount = x 1 + x2 - x1 × x2 % 100

 = 20 + 20 - 20 × 20 % 100

= 40 - 4
= 36 %

Trick 2: Single discount equivalent to three successive discount x1 %, x2 % and x3 %.

 Selling price = 1 - 1 - x1 × 1 - x2 × 1 - x3 × 100% 100 100 100

Example: What is the single equivalent discount for successive discount of 40 % , 30 % and 20 % on marked price of an article.
Solution:- Let x1 = 40 %
x2 = 30 %
x3 = 20 %

 Selling price = 1 - 1 - x1 × 1 - x2 × 1 - x3 × 100% 100 100 100
 = 1 - 1 - 40 × 1 - 30 × 1 - 20 × 100% 100 100 100
 = 1 - 1 - 2 × 1 - 3 × 1 - 1 × 100% 5 10 5
 = 1 - 3 × 7 × 4 × 100% 5 10 5
 = 1 - 84 × 100% 250
 = 250 - 84 × 100% 250
 = 166 × 100% 250

= 66.4 %

Example: A shopkeeper marked the price 20 % more than its cost price. If he allows a discount of 30 %, then find his loss per cent.
Solution: Let the cost price = 100
then marked price = 120
discount price = 30 % of 120

 = 30 × 120 100

= 36

 Marked price = selling price + Discount

= 120 - 36
= 84

 Loss = Cost Price - Sale Price

= 100 - 84
= 16
 Loss % = Loss × 100 CP
 = 16 × 100 100

= 16 %