PROFIT AND LOSS

When we face problems on profit and loss, there is need to understand what cost price (c.p) and selling price (s.p) are.

Cost Price (C.P):
It is the price at which an item is bought at a particular period.

Selling Price (S.P):
The price at which an item is sold at a particular period

Profit:
When the selling price is greater than cost price the variance between them becomes the profit.

Loss:
If the price is more than selling price, the difference between them becomes the loss

Profit Percentage:

P%= {(profit/c.p) x 100}%

Loss Percentage:

L% = {(loss/c.p) x 100}%

Example:

1. A bottle of cashew nut is sold at $50 and there has been a loss of 10 percent of the selling price. What is the cost of a bottle of cashew nut?

Solution:

Cost price - Loss = Selling Price
Cost Price = Selling Price + Loss
Loss = 10% of the selling price
         = 10 x 50/100
         = $5
Cost  = 50 + 5 =$55
The cost of a bottle of cashew nut = $55

2. Mr John bought a T-shirt for $750 and sold it at a profit of 40 percent of the selling price.
What is the Selling Price?

Solution:

Let the Selling Price = x
Profit  = 40% of selling price
           = 40% of x = 0.4x
Cost + Profit = Selling Price
  750 + 0.4x  =  x
      x + 0.4x  = 750
            0.6x  = 750
Dividing Through with 0.6
                 x  = 750/0.6
                 x  = $1250

 Mr John sold the T-shirt at $1250

3. Yogurt cost $15 and it is sold at $20. What is the percent of profit based on cost price?

Solution:
Cost + Profit = Selling Price
            Profit = Selling Price - Cost
                      = 20 - 15 = $5
% of profit based on cost price = {(Profit/cost Price) x 100}%
                                                  = 5/15 x 100
                                                  = 33%
i.e. 33% profit based on cost price

Note: If the profit is based on the selling price
% of profit based on selling price = {(Profit/Selling Price) x 100}%
                                                      = 5/20 x 100
                                                      = 25%
 i.e 25% profit based on selling price

4. The cost price of an apple is $4 and there is a discount of 3 percent.
    What is the selling price?

Solution:

Discount  = 100 - 3
                = 97% = 0.97
Selling Price = 0.97 x 4
                      = $3.88

OR

3% Discount = 4 x 3/100 = $0.12
 Cost - Loss  = Selling Price
Selling Price = 4 - 0.12
                      = $3.88