FIND THE SELLING PRICE IF WE WANT TO MAKE A GIVEN PROFIT OR LOSS

Find the Selling Price if we Want to Make a Given Profit or Loss :

In this section, we will see how to solve problems with the concept of profit and loss.

Formulas Used in Profit and Loss

Profit (or) gain  =  Selling price - Cost price

Loss  =  Cost price - Selling price

Profit %  =  (Profit / Cost price) ⋅ 100

Loss %  =  (Loss / Cost price) ⋅ 100

Cost price  =  [100 / (100 - loss%)] ⋅ Selling price

Cost price  =  [100 / (100 + profit%)] ⋅ Selling price

Selling price  =  [(100 + profit%)/100] ⋅ Cost price

Selling price  =  [(100 - loss%)/100] ⋅ Cost price

Find the Selling Price if we Want to Make a Given Profit or Loss - Examples

Example 1 :

A fruit seller sells mangoes at the rate of $9 per kg and there by losses 20%. At what price per kg, he should have sold them to make a profit of 5% ?

Solution :

Let x be the cost price.

Selling price  =  $9 per kg

x - 20% of x  =  9

80% of x  =  9

x  =  9/0.80

x  =  11.25

To make 5% profit, the selling price will be

  =  105% of 11.25

  =  1.05(11.25)

  =  11.81

Example 2 :

A property dealer sells a house for $630000 and in the bargain makes a profit of 5%. Had he sold it for $500000 then what percentage of loss or gain he would have made ?

Solution :

Selling price of a house  =  630000

Let x be the cost price.

105% of x  =  630000

x  =  630000/1.05

x  =  600000

So, the cost price is  600000. 

New selling price  =  500000

Cost price  >  selling price

Loss  =  Cost price - Selling price

Loss  =  100000

Loss %  =  (Loss / Cost price)⋅100

  =  (100000/600000)⋅100

  =  16.67%

Example 3 :

A shopkeeper sells one transistor for $840 at a gain of 20% and another for $960 at a loss of 4%. His total gain or loss percent is :

Solution :

Let x be the cost price.

Selling price of one transistor  =  $840

120% of x  =  840

x  =  840/1.20

x  =  700

Selling price of another transistor  =  $960

96% of x  =  960

x  =  960/0.96

x  =  1000

Total cost of two transistors  =  700 + 1000

=  1700

Total selling price  =  840 + 960

=  1800

Selling price > Cost price

profit  =  1800 - 1700

Profit  =  100

profit %  =  (profit / Cost price)⋅100

=  (100/1700)⋅100

=  5.88%

After having gone through the stuff given above, we hope that the students would have practiced problems in profit and loss.

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