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Published on January 31st, 2011 In category Education | Maths

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Problem solving- items sold on discount

In the MBA enterance examination the problem solving section often ask the problems based on discount, profit and loss. The best way to solve these problems and approach to the solutions is as follows:

The problem: A shopkeeper makes 20 % gross profit even when he is selling the a carpet on 20 % discount. What was his gross margin when he was selling item without any discount?

Lets assume the regualr price of carpet is Rs. 100. When he is selling at 30 % discount the price will be Rs. 80. He still making a profit of 80 %. If the Cost Price of carpet is X, the discounted selling price is 1.20 x = 80    hence x = 800/12 = 200/3

So the gross margin = Selling price (without discount) – Cost Price =   (100)  – (200/3) = 100/3

% margin = Profit/Cost price   x 100  =  (100/3) / (200/3)  = 50 %

Some general formula can be deducded as follows:

If  m % is the mark up %,  d% is the discount % and p% is the profit %, then

Mark-Up is price at which product is sold without discount or orginal selling price

Selling price is price at which it is actually sold.

Marked Price (MP) = cost price (CP)  x ( 1 + m/100)

Selling price (SP)  =  MP x (1 – d/100) = which means: CP x ( 1 + m/100) x (1 – d/100) = SP
We know, CP x (1 + p/100) = SP

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