Recently we have discussed about Profit and Loss shortcut formulas and questions, this time we will be discussing discount formulas and questions with answers

What is discount?

Discount is a rebate which the shopkeeper gives to their customers on selling some goods.

Note: Discount is always calculated on Print Rate (PR)

Here are some important rules and facts of discounts.

· Selling price (SP)= Print rate – Discount

· If the rate of discount is r%, then

SP= PR*{(100-r)/100}

· If a shopkeeper wants to make a profit of R% and also gives discount of r%, then

PR= CP*{(100+R)/(100-r)} where CP= Cost Price

· If an item is sold on consecutive discounts of r1 %, r2 %, r3 %, then

SP= PR[{(100-r1)/100}{(100-r2)/100}{(100-r3)/100}]

And if SP of the price is given then

PR= CP{(100*100*100)/(100-r1)(100-r2)(100-r3)}

· If a shopkeeper wants to make a profit of R% and also gives discount of r%, then that shopkeeper should write PR more than the CP by [100(r+R)/(100-r)]

· If on selling an item, there are two discounts of r% and R% given on the item, then SP of the item should be

SP= PR[{(100-r)/100}{(100-R)/100}]

· If there are two discounts on an item of r% and R%, then equivalent discount to both of these discounts will be

= {r+R-(rR/100)}

Example:1

A shopkeeper has an item which has a print rate of 3500. The shopkeeper sold that item with 40% profit after giving a discount of 20%, find the CP of the item?

Solution:

Now r= 20%

and R=40%

PR= 3500

Now formula for CP

CP= PR[(100-r)/(100+R)]

CP= 3500[(100-20)/(100+40)]

CP= (3500*80)/140

CP= 2000

Example:2

Find the equivalent discount (ED) to consecutive discounts of 20% and 30%.

Solution:

ED= r+R-(rR/100) %

ED= 20+30-{(20*30)/100} %

ED= 50-6=44 %

Hope you understand all the formulas given above and can solve the discount problems better.

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