## 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 % = | × 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 % = | × 100 | |

Marked price |

= | × 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 x_{1}%, x_{2}%, x_{3}%……….. 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 - | _{1} |
× | 1 - | _{2} |
× | 1 - | _{3} |
||||||

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

x_{1} = 20 %

x_{2} = 10 %

x_{3} = 5 %

Selling Price = M | 1 - | _{1} |
× | 1 - | _{2} |
× | 1 - | _{3} |
||||||

100 | 100 | 100 |

= 5000 | 1 - | × | 1 - | × | 1 - | |||||||||

100 | 100 | 100 |

= 5000 | 1 - | × | 1 - | × | 1 - | |||||||||

5 | 10 | 20 |

= 5000 | × | × | × | = 5 × 4 × 9 × 19 | |||

5 | 10 | 20 |

= 20 × 171

= ₹ 3420

Some Useful Shortcut Method

**Trick 1:** Single discount equivalent to two successive discounts x_{1}% and x_{2}%

Single Equivalent discount = x _{1} + x_{2} - |
x_{1} × x_{2} |
% | ||

100 |

**Example:** What will be the single equivalent discount for successive discount of 20 % and 10 %.
**Solution **: given x_{1} = 10 %

x_{2} = 20 %

Single Equivalent discount = x _{1} + x_{2} - |
x_{1} × x_{2} |
% | ||

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 x_{1} = 20 % & x_{2} = 20 %.

Single Equivalent discount = x _{1} + x_{2} - |
x_{1} × x_{2} |
% | ||

100 |

= 20 + 20 - | 20 × 20 | % | ||

100 |

= 40 - 4

= 36 %

**Trick 2:** Single discount equivalent to three successive discount x_{1} %, x_{2} % and x_{3} %.

Selling price = | 1 - | 1 - | x_{1} |
× | 1 - | _{2} |
× | 1 - | _{3} |
× 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 x_{1} = 40 %

x_{2} = 30 %

x_{3} = 20 %

Selling price = | 1 - | 1 - | x_{1} |
× | 1 - | _{2} |
× | 1 - | _{3} |
× 100% | ||||||||

100 | 100 | 100 |

= | 1 - | 1 - | 40 | × | 1 - | × | 1 - | × 100% | ||||||||||

100 | 100 | 100 |

= | 1 - | 1 - | 2 | × | 1 - | × | 1 - | × 100% | ||||||||||

5 | 10 | 5 |

= | 1 - | 3 | × | × | × 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 %

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