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Loss or profit percentage is one of the most important concepts in mathematics that can prove to be highly useful in day-to-day life. The process of calculating percentage loss or gain is greatly required in the fields of business and economics. In addition, many financial and statistical methods are also essentially based on this particular formula. This is especially used to calculate the percentage loss or gain of an investment by the buyers, resorting to finding out the purchase price using the loss and profit percentage formula. The loss in any investment can be demonstrated in the form of percentage using this formula.
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Key Terms: Loss, Percentage, Formula, Gain, Financial, Statistical, Purchase Price, Profit
Loss Percentage Formula
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When it so happens that the cost price of an object is more than the selling price, there occurs a loss. In other words, when CP (Cost Price) > SP (Selling Price), there occurs a loss. Therefore,
Loss = Cost Price (CP) – Selling Price (SP).
Accordingly,
Loss Percentage (%) = LossCP x 100%
Other Important Loss and Profit Percentage Formula
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There are some important definitions and formulae one has to be aware of while entering into the financial world of loss and profit. They are as follows.
- Cost Price (CP): The cost price of an object is the price at which an object is bought or purchased.
- Selling Price (SP): The price at which an object is sold is known as the selling price.
- Profit or Gain: If the price at which an object is sold (Selling Price or SP) is more than the price at which the same object is purchased (Cost Price or CP), the difference between them is known as the profit. This can be represented by the following formula:
Profit = SP – CP
- Loss: If the selling price is less than the cost price, the difference between them is known as the loss. This is represented by the following equation:
Loss = CP - SP
- Marked Price or List Price: The marked price or the list price is the price at which the selling price of an object is made a note of on the object.
- Discount: The price that is offered to the customer as a discount or a rebate or a concession on the object is known as the discount.
- Profit Percentage (%): ProfitCP x 100%.
- Loss Percentage (%): LossCP x 100%.
These can also be represented in other forms as given below.
- Cost Price or CP = 100100 + Gain x SP.
- Selling Price or SP = 100 + Gain100 x CP.
- Cost Price or CP = 100100 - Loss x SP.
- Selling Price or SP = 100 - Loss100 x CP.
The main advantage of learning profit and loss percentage formulas is that these are not only constrained to high school education but can also appear quite needy in later life as well. Not only are they asked directly in competitive exams like CAT, GRE, UPSC, IBPS, GMAT, etc., but they are also highly necessary while learning courses on business administration where there are papers on financial statements, trading, accounting, stock market, etc.
Things to Remember:
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- When CP (Cost Price) > SP (Selling Price), there occurs a loss and when SP > CP, there occurs a profit.
- Important Formulas related to Profit and Loss:
Profit Percentage (%): ProfitCP x 100%.
Loss Percentage (%): LossCP x 100%.
Cost Price or CP = 100100 + Gain x SP.
Selling Price or SP = 100 + Gain100 x CP.
Cost Price or CP = 100100 - Loss x SP.
Selling Price or SP = 100 - Loss100 x CP.
Sample Questions:
Ques. A carrom board is given 10% and 5% discounts in a row and is sold at Rs. 513. What is the market price or the list price of the board? (2 marks)
a)560
b)270
c)600
d)852
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Ans.
Let Ï° be the market price of the shoes. Giving discounts to the customer is essentially a loss for the seller. Therefore, as given,
100 - 10100 x 100 - 5100 x Ï° = 513.
90100 x 95100 x Ï° = 513. Therefore,
Ï° = 600.
So, the market price of the said carrom board is Rs.600.
Ques. A seller of sports utilities had to bear a loss in a deal that is 4/7th of the selling price. What is the loss in percentage? (3 marks)
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Ans. Let Ï° be the selling price of the items. Therefore,
Loss = 3Ï°5. Taking the loss percentage formula in the equation,
Loss Percentage (%) = LossCP x 100%
CP = SP + loss
= Ï° + 3Ï°5
= 8Ï°7. Therefore,
Loss = 37.5%.
Ques. If the cost price of an object is Rs. 60 and the selling price of the same object is Rs. 55, find out the loss and the loss in percentage. (2 marks)
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Ans.
As given,
CP = 60
SP = 55. We know that,
Loss = CP – SP
= 60 – 55
= 5.
Therefore, the loss is Rs. 5.
Again, we know,
Loss Percentage (%) = LossCP x 100%
= 560 x 100%
= 8.33%
Therefore, the loss percentage is 8.33%.
Ques. When Achyuth sold a chair for Rs. 940, he lost 6%. What is the cost price of the chair? Find out using the loss percentage formula. (2 marks)
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Ans.
As given,
Loss Percentage = 6%
SP = 940
If CP is 100, then SP is 94. Therefore, when SP is 94,
CP = 100. Likewise, when SP is 900,
CP = 10094 x 940.
= 1000.
Therefore, the cost price of the chair is Rs. 1000.
Ques. Archana bought a scooter for Rs. 25000. If she sold it at a loss of 10%, what price did she sell it for? (2 marks)
a)26600
b) 26000
c)22500
d)23400
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Ans. c. 22500
Ques. Amarnath bought a home theatre set for Rs. 15,200 and sold it at a loss of 20%. Find out the selling price of the home theatre set? (2 marks)
a)Rs. 13,120
b) Rs. 12,108
c)Rs. 12,209
d)Rs. 12,160
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Ans.
As given,
Loss Percentage = 20%
CP = 15200
Loss = (20)/(100) x15200
= Rs. 3040. We know that,
SP = CP – Loss
= 15200 – 3040
= 12160
Therefore, the selling price of the home theatre set is Rs. 12160.
Ques. Priyatha sold two necklaces at Rs 594 each. On one she gained 10% and on the other, she lost 10%. What is her gain or loss percent in total? (4 marks)
a)1%
b)2%
c)3%
d)Data is not sufficient
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Ans. As given,
SP of the first necklace = 594
Gain percentage = 10%. Therefore,
CP of the first necklace = [100/(100 + profit percentage)] x SP
= [100/(100 + 10)] x 594
= 540.
Likewise,
CP of the second necklace on which she lost 10% = [100/(100 – Loss percentage)] x SP
= [100/(100 -10)] x 594
= (100/90) x 594
= 660
Total CP of the two necklaces = 540 + 660
= 1200
Total SP of the two necklaces = 594 + 594
= 1188. Therefore,
Net Loss = 1200 – 1188
= Rs. 12. Thus,
Loss percentage = [Loss/C.P.] x 100.
= {(12/1200)} x 100
= 1%.
Therefore, the right answer is a. 1%.
Ques. Suppose Sidharth’s company produces 1000 speakers in the year 2021 and 1200 speakers in the year 2022. On the other hand, Gayathri’s company produces 5000 speakers in the year 2021 and 5500 speakers in the year 2022. Which company has the better growth rate? (2 marks)
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Ans. Look at Sidharth’s company. The increase is of 200 speakers and for Gayathri’s company, the increase is of 500 speakers. So, in terms of numbers, Sidharth’s company has produced less than Gayathri’s company. But here, we need the result in terms of relative growth, i.e., growth with respect to its previous year production. Taking that point into consideration, the growth of Sidharth’s company with respect to its previous year production
will be (200/1000)×100 = 20%. And that for Gayathri’s company, it will be (500/5000)×100 = 10%. So clearly Sidharth’s company has a better growth rate than Gayathri’s company.
Ques. Vyshakh sells a fish bowl for Rs. 1200. and he makes a profit of 20% in the deal. Find out the cost price? (3 marks)
a)Rs. 500
b)Rs. 1000
c)Rs. 1500
Rs. 2000
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Ans.
Let CP be Ï°. Now,
SP = Ï° + 20%(Ï°)
= 1.2 Ï°.
SP = 1200
1200 = 1.2 Ï°
Ï° = 1000
CP = Rs. 1000.
Therefore, the right answer is b. Rs. 1000.
Ques. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is: (2 marks)
a)15
b)16
c)18
d)25
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Ans. B
Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
| 20 - x | x 100 = 25 |
| x |
2000 - 100x = 25x 125x = 2000 x = 16.
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