Calculating Profit Percent and Loss Percent

In calculating profit percent and loss percent we will learn about the basic concepts of profit and loss. We will recall facts and formula while calculating profit percent and loss percent. Now we will apply the concept of percentage to find profit/loss in selling and buying of goods in our day to day life.

Cost price (CP)       The amount for which an article is bought is called its cost price.

Selling price (SP)   The amount for which an article is sold is called its selling price.

Profit or gain          When (SP) > (CP) then there is a gain.

                                 Gain = (SP) - (CP)

Loss                         When (SP) < (CP) then there is a loss.

                                 Loss = (CP) - (SP).

Notes: 

The gain or loss is always reckoned on the cost price

Calculating Profit Percent and Loss Percent

Profit and loss formulas for calculating profit% and loss%:

I. Gain = (SP) - (CP)

II. Loss = (CP) - (SP)

III. Gain% = (\(\frac{gain}{CP}\) × 100)%

IV. Loss % = (\(\frac{loss}{CP}\) × 100)%

V. To find SP when CP and gain% or loss% are given:

● SP =  [(100 + gain %) / 100] × CP 

\[SP = \frac{100 + gain  ٪}{100}\times CP\]

● SP = {(100 - loss %) /100} × CP

\[SP = \frac{100 - loss  ٪}{100}\times CP\]

VI. To find CP when SP and gain% or loss% are given:

● CP = {100/(100 + gain %)} × SP

\[CP = \frac{100}{100 + gain ٪}\times SP\]

● CP = {100 /(100 - loss %)} × SP

\[CP = \frac{100}{100 - gain ٪}\times SP\]

Calculating Profit Percent and Loss Percent

Worked-out problems on calculating profit percent and loss percent:

1. Mike bought a DVD for $ 750 and sold it for $ 875. Find Mike's gain per cent. 

Solution: 

CP = $ 750 and SP = $ 875. 

Since (SP) > (CP), Mike makes a gain. 

Gain = $ (875 - 750) 

        = $ 125. 

Gain% = {(gain/CP) × 100} %

           = {(125/750) × 100} % 

           = (50/3) % 

           = 16 (2/3) % 

2. Ron purchased a table for $ 1260 and due to some scratches on its top he had to sell it for $ 1197. Find his loss per cent. 

Solution: 

CP Rs.1260 and SP = $ 1197. 

Since (SP) < (CP), Ron makes a loss. 

Loss = $ (1260 - 1197) 

       = $ 63. 

Loss % = [(loss / CP) × 100] %

             = [(63 / 1260) × 100] % 

             = 5%


In calculating profit percent and loss percent, sometimes after purchasing an article, we have to pay some more money for things like transportation, repairing charges, local taxes, These extra expenses are called overheads. 

For calculating the total cost price, we add overheads to the purchase price. 

3. Maddy purchased an old scooter for $ 12000 and spent $ 2850 on its overhauling. Then, he sold it to his friend Sam for $ 13860. How much per cent did he gain or lose? 

Solution: 

Cost price of the scooter = $ 12000, overheads = $ 2850. 

Total cost price = $ (12000 + 2850) = $ 14850. 

Selling price = $ 13860. 

Since (SP) < (CP), Maddy makes a loss. 

Loss = $ (14850 - 13860) = $ 990. 

Loss = [(loss / total CP) × 100] % 

       = [(990 / 14850) × 100] % 

       = 6 

4. Ron ought an almirah for $ 6250 and spent $ 375 on its repairs. Then, he sold it for $ 6890. Find his gain or loss per cent. 

Solution:

CP of the almirah = $ 6250,

Overheads = $ 375.

Total cost price = $ (6250 + 375)

                       = $ 6625.

Selling price = $ 6890.

Since, (SP) > (CP), Ron gains.

Gain% = $ (6890 - 6625)

           = $ 265.

Gain% = [(gain / total CP) × 100] %

          = [(265 / 6625) × 100] %

          = 4 %

5. A vendor bought oranges at 20 for $ 56 and sold them at $ 35 per dozen. Find his gain or loss per cent.

Solution:

LCM of 20 and 12 = (4 × 5 × 3) = 60.

Let the number of oranges bought be 60.

CP of 20 oranges = $ 56

CP of 1 orange = $ (56 / 20)

CP of 60 oranges = $ [(56 / 20) × 60] = $ 168

SP of 12 oranges = $ 35

SP of 1 orange = $ [(35 / 12) × 60] = $ 175

Therefore, CP = $ 168 and SP = $ 175.

Since, (SP) > (CP), the vendor gains.

Gain = $ (175 - 168) = $ 7.

Gain % = [(gain / CP) × 100] %

           = [(7 / 168) × 100] %

           = 25 / 6 %

           = 4 ¹/₆ %

6. If the cost price of 10 pens is equal to the selling price of 8 pens, find the gain or loss per cent.

Solution:

Let the cost price of each card be $ x

Then, CP of 8 pens = $ 8x.

SP of 8 pens = CP of 10 pens = $ 10x.

Thus, CP = $ 8x and SP = $ 10x.

Since, (SP) > (CP), there is a gain.

Gain = $ (10x - 8x) = $ 2x.

Gain % = [(gain / CP) × 100] %

           = [(2x / 8x) × 100] %

           = 25%

PROFIT AND LOSS PERCENT

Mostly we express the profit and loss per cent. We calculate the profit and loss per cent as below.

Profit per cent = \(\frac{Profit}{Cost Price}\) × 100

Loss per cent = \(\frac{Loss}{Cost Price}\) × 100

Let us consider some more examples.

7. The cost price of a power bank is $25. Nairitee sold it to her sister Nithyyea at $30. Find the profit per cent.

Solution:

Cost price of the pen = $25

Selling price of the pen = $30

Profit = S.P. - C.P.

         = $30 - $25

         = $5 

Profit per cent = \(\frac{Profit}{Cost Price}\) × 100 %

                     = \(\frac{5}{25}\) × 100 %

                     = \(\frac{500}{25}\)%

                     = 20%

Therefore profit percent = 20%

8. Richard bought a bicycle for $200 and sold for $175. Find the profit or loss percent.

Solution:

Cost price of the bicycle = $200

Selling price of the bicycle = $175

Loss = C.P. - S.P.

       = $200 - $175

       = $25

Loss percent = \(\frac{Loss}{Cost Price}\) × 100%

                   = \(\frac{$ 25}{$ 200}\) × 100%

                   = \(\frac{2500}{200}\)%

                   = \(\frac{25}{2}\)%

                   = 12\(\frac{1}{2}\)%

Therefore, loss percentage = 12\(\frac{1}{2}\)%

9. The cost price of a washing machine is $450. Christopher sold it to to his brother Anthony at 20% profit. Find the selling price.

Solution:

Cost price of the washing machine = $ 450

Profit = 20% of the C.P.

        = 20% of $450

        = \(\frac{20}{100}\) × $450

        =  \(\frac{1}{5}\) × $450

        = $\(\frac{450}{5}\)

        = $90

Selling price = Cost price + Profit

                  = $450 + $90

                  = $540

Therefore, selling price = $540.

10. The cost price of a bluetooth speaker is $450. The shopkeeper sold it at 12% loss. Find the selling price of the bluetooth speaker.

Solution:

Cost price of the bluetooth speaker = $450

Loss = 12% of C.P.

12% of $450 = \(\frac{12}{100}\) × $450

                   = $ \(\frac{12 × 450}{100}\)

                   = $ \(\frac{5400}{100}\) 

                   = $ 54

Selling price = Cost price - Loss

                  = $405

Therefore, the selling price of the bluetooth speaker = $405

11. A bookseller bought some books at the rate of $85 per book and sold them at the rate of $90.50. Find his profit percent on each book.

Solution:

Cost price of each book = $85

Selling price of each book $90.50

Profit per book = $90.50 - $85

                      = $5.50

Profit percent = \(\frac{Profit}{Cost price}\) × 100%

                    = \(\frac{$5.50}{$85}\) × 100%

                    = \(\frac{$5.50 × 100}{$85}\)%

                    =  \(\frac{$550}{$85}\)%

                    =  \(\frac{$550}{$85}\)%

                    =  \(\frac{110}{17}\)%

                    =  6\(\frac{8}{17}\)%

Therefore, profit = 6\(\frac{8}{17}\)%

● Profit, Loss and Discount

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Discount

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

7th Grade Math Problems

8th Grade Math Practice 

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