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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)
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)
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)
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.
● 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
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
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