Conversion, Profit & Loss, Simple Interest

KAPDEC® | Elite STEM Learning Platform | https://kapdec.com

Algebra: Comparing Quantities

Profit or Loss as a Percentage:

Profit and Loss:  In our daily life, we buy goods from the shopkeepers in the market which they buy either directly from manufacturers or through wholesalers.

Source: Kapdec.com

In order to earn money, the shopkeepers sell goods at a rate which is higher than the rate at which they purchased them.

Cost Price: The money paid by the shopkeeper to buy the goods from a manufacturer or a wholesaler is called the cost price of the shopkeeper and denoted by C.P.

Selling Price: The price at which a shopkeeper sells the goods is called the selling price of the shopkeeper, and it is denoted by S.P.

Profit: If the selling price of an article is greater than cost price, then the shopkeeper makes a gain or profit, and the amount of profit is equal to the difference between the selling price and the cost price.

Thus, if S.P. > C.P.           Profit = Sell price – Cost price

Loss:  If the selling price of an article is less than the cost price then the shopkeeper suffers a loss, and the amount of loss is equal to the difference between the cost price and the selling price.

Thus, if S.P. < C.P., then.

Loss= cost price – sale price

Example: If the cost price of an article is $20 and the selling price is  $30,  find the profit on the sold article.

Solution:We have,

Cost price= $20

Sell price =$30

Thus, profit= sale price – cost price

Profit= 30- 20 = $10

Example: If the cost price of an article is $65 and the selling price is $50, find the profit or loss on the whole transaction.

We have,

 Cost price =$65

Sell price= $50

We say that the cost price is greater than the sale price, so there is a loss on the whole transaction.

Thus, Loss = cost price- sell price

Loss= 65- 50= $15

Profit Percent and Loss Percent: 

In order to compare the profit or loss on the transaction, we usually express profit and loss as a percent of the cost price.

The profit percentage is the profit that would be obtained for a C.P. of $ 100.

Similarly, the loss percentage is the loss that would be made for a C.P. of $100

                                   Profit %= ProfitsC.P.

Source: Kapdec.com

 × 100

                                    Loss% = LossC.P.

Source: Kapdec.com

 × 100

Source: Kapdec.com

Example:  If cost price =$1120, sale price= $1260

Then profit%=?

We have,cost price =$1120

Sell price= $1260

Profit= 1260-1120= $140

Profit %= ProfitsC.P.

Source: Kapdec.com

 × 100

Profit% =  1401120

Source: Kapdec.com

 × 100 = 12.5%

Example:

If the sell price = $30 and cost price = $40 then, find loss%:

We have,sell price = $30

Cost price= $40

Loss = 40 -30 = $10

Loss% = LossC.P.

Source: Kapdec.com

 × 100

 Loss% = 1040

Source: Kapdec.com

 × 100 = 25%

Example: If the cost price of 6 apples is equal to the selling price of 5 apples. Find the profit percentage.

Solution:Let the cost price of each apple be $1

Then, CP of 5 apples = $5

SP of 5 apples = CP price of 6 apples = $6

Profit = SP – CP = 6-5 = $1

Source: Kapdec.com

Example: By selling a TV for $240, a seller’s profit is 20%. Find the cost price of the TV.

Solution:Let the CP be$100

Then, SP = $(100+20) = $120

If the SP is $120, then CP = $100

Source: Kapdec.com

Some useful formula:

Some useful formula:

S.P. = 100+profit or gain%100

Source: Kapdec.com

  × C.P.

S.P. = 100-Loss %100

Source: Kapdec.com

  × C.P.

C.P. = 100100+gain%

Source: Kapdec.com

  × S.P.

C.P. = 100100-loss%

Source: Kapdec.com

  × S.P.

**Students are advised to remember the above formula because it will be helpful in solving various difficult problems of profit and loss.

Key Point:   

The profit or loss incurred in a certain transaction can be expressed in terms of percentages