DISCOUNT PROBLEMS IN PROFIT AND LOSS

Problem 1 :

An retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the market price. What is his actual profit on the sales ?

Solution :

Let x be the cost price.

Marked price  =  150% of x  =  1.5x

profit  =  25% of x  =  0.25x

Discount made  =   25% of marked price

  =  25% of 1.5x

=  0.375x

Selling price after discount made  =  1.5x - 0.375x

  =  1.125x

Profit  =  Selling price - Cost price

=  1.125x - x

=  0.125x

Profit%  =  (Profit/Cost price)⋅100

=  (0.125x/x) ⋅ 100

=  0.125 (100)

=  12.5 %

So, the actual profit is 12.5%.

Problem 2 :

A retailer buys 40 pens at the marked price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent ?

Solution :

Let $1 be the cost of 1 pen.

Then,

Cost price of 40 pens  =  $36

Discount  =  1%

  =  1% of 40

  =  0.4

Selling price after discount  =  40 - 0.4

  =  39.6

Profit  =  Selling price - Cost price

Profit  =  39.6 - 36

profit  =  3.6

Profit %  =  (3.6/36)⋅100

Profit  =  10%

So, the required profit is 10%

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