Percentage loss is a pivotal concept in this section. Many examples are directly or indirectly based on the concept of Percentage loss. In the following section, we will recall all the important concept of this section. We will also see how we can represent the loss in the form of a percentage. We have solved examples and practice questions. Let us see further!

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## Percentage Loss

Profit and loss is the branch of basic mathematics which deals with the study of profit and loss made in a business transaction. The profit and loss account is fundamentally a summary of the trading transactions of a business and shows whether it has made a profit or loss during a particular period of account. Indeed, by deducting the total expenditure from total income the profit or loss of a business can be calculated. Along with the balance sheet, it is one of the key financial statements that make up a company’s statutory accounts. Basically, this type of account shows the following information for a business:

- Sales revenue earned by business.
- Cost of sales that the business has incurred.
- Other operating costs incurred by the business.
- Profit/Loss earned by business.

**Browse more Topics under Profit And Loss**

- Cost Price
- Fixed, Variable and Semi-variable Cost
- Selling Price
- Marked Price
- List Price
- Margin
- Dishonest Dealers and Faulty Weights
- Percentage Gain
- Discounts and Marked Price
- Equivalent Discount
- Equation-Based Questions
- Goods Passing Through Successive Hands
- True Discount
- Bankers Discount
- Profit and Loss Practice Questions

Profit and loss are mainly used in finance and business transactions. Some important profit and loss formulas are:

Notations used in profit and loss: S.P. is Selling price,Â C.P. for Cost price, and M.P. for Marked Price

### Important Formulas

Following are the important formulas of the section. Note that you will have to master all of them before you proceed any further.

- Profit or Gain = Selling price â€“ Cost price
- Loss = Cost price â€“ Selling price
- Profit Percentage = [Profit/C.P.]Ã—100
- Percentage Loss = [Loss/C.P.]Ã—100

Example 1:Â The price of a house is decreased from Rupees Fifteen lakhs to Rupees Twelve lakhs. Find the percentage of decrease.

A) 15%Â Â Â Â Â Â Â Â Â Â Â B) 20%Â Â Â Â Â Â Â Â Â Â C) 25%Â Â Â Â Â Â Â Â Â Â Â Â Â D) 30%

Answer:Â Original price = Rs 15,00,000

Change in price = Rs 12,00,000

Decrease in price = 15,00,000 â€“ 12,00,000 = Rs. 3,00,000

Therefore, the percentage of decrease = (3,00,000)/(15,00,000)Ã—100 = 20%.

While calculating the percentage increase or decrease remember the following formulas:

Percentage of increase = (Increase in amount)/(Original amount)Ã—100

Percentage of decrease = (Decrease in amount)/(Original amount)Ã—100

Example 2:Â Hameed buys a colour T.V set for Rs. 15,200 and sells it at a loss of 20%. What is the selling price of the T.V set?

A) Rs. 13,120Â Â Â Â Â Â B) Rs. 12,108Â Â Â Â Â Â C) Rs. 12,209Â Â Â Â Â Â Â Â D) Rs. 12,160

Answer: Here we will see two methods that we can use to solve this problem. Let us focus on the first method and then the second one.

First Method:Â Loss is 20% of the C.P., then we have = (20)/(100) Ã—15200Â = Rs. 3040

S.P. = C.P. â€“ Loss = Rs. (15,200 â€“ 3,040). In other words, we can say that the S. P. of the TV must have been = Rs. 12,160. Hence the correct option is Rs. 12,160.

Second Method:

We have the C.P. = Rs. 15,200.

Loss is = 20%. Therefore we have the S.P. = [(100 – Loss%)/100]Ã— C. P.

Which can be simplified and written as = [(100 – 20)/100]Â Ã— 15200.

In other words we may write, = {80/100}Â Ã— 15200 = Rs. 12,160

Let us now see some solved examples on the concept of percentage loss.

## Solved Examples For You

Example 3:Â A scooty is sold for Rs. 13,600 and fetches a loss of 15%. Find the cost price of the scooty.

A) 12000Â RsÂ Â Â Â Â Â B) 14000Â RsÂ Â Â Â Â Â Â Â Â C) 16000Â Rs Â Â Â Â Â Â Â Â Â D) 18000Â Rs

Answer: First Method: Let us start with loss percentage. Here the loss 15% which means that if C.P. is Rs 100, the loss will be Rs. 15. Therefore, S.P. would be (Rs 100 – Rs 15) = Rs 85.

If S.P. is Rs. 85, then C.P. is Rs. 100. Now, when S.P. is Rs 13,600, then the C.P. will be equal to =

(100Ã—13600)/85 = Rs 16,000. Hence the cost price is Rs 16,000 and the correct option isÂ C) Rs 16000.

Second Method: Here loss = 15%. and S.P. = Rs. 13,600

Therefore, the C.P. = {100/(100 – Loss percentage)}Â Ã— S.P. which can be written as:

= {100/(100 – 15)}Ã—13,600 = Rs. 16,000.

Example 4:Â A man sells two wrist watches at Rs 594 each. On one he gains 10% and on the other, he loses 10%. Find his gain or loss percent on the whole.

A) 1%Â Â Â Â Â Â Â Â Â Â Â B) 2%Â Â Â Â Â Â Â Â Â Â C) 3%Â Â Â Â Â Â Â Â Â Â Â Â D) Data is not sufficient

Answer:Â Given: S.P. of the first wristwatch = Rs. 594, Gain percentage = 10%

Therefore, the C.P. of the first wristwatch = [100/(100 + profit percentage.)]Ã— S. P.

This can be written as: [100/(100 + 10)] Ã— 594 = Rs. 540.

Similarly, C.P. of the second watch on which he loses 10% is = [100/(100 – Loss percentage)]Ã—S. P.

In other words, we can write = [100/(100 -10)]Ã—594 = (100/90)Ã— 594 = Rs. 660.

To say whether there was an overall Profit or Loss, we need to find the combined C.P. and S.P.

Total C.P. of the two watches = 540 + 660 = Rs 1,200.

Total S.P. of the two watches = 594 + 594 = Rs 1,188.

Therefore, Net Loss = Rs. 1,200 â€“ Rs. 1,188 = Rs. 12.

Thus the Loss percentage = [Loss/C.P.]Ã—100. On substitution of the relevant values, this equation becomes:

Loss percentage = {(12/1200)}Ã—100 = 1%. Hence the correct option is A) 1%.

## Practice Questions:

Q 1: A shopkeeper sells a book at a discount of 10%. He earns a profit of 12%. Then the ratio of the C.P. to the marked price of the book is?Â Â Â Â Â Â [SSC – CGL,2013]

A) 33: 31Â Â Â Â Â Â Â Â Â Â Â Â B) 3: 2Â Â Â Â Â Â Â Â Â Â Â Â C) 45: 56Â Â Â Â Â Â Â Â Â Â Â D) 2:3

Ans: C) 45: 56

Q 2: A shopkeeper sells a gold bangle and a diamond necklace for Rs 10,000 each. On one of the items he losesÂ 20% and on the other item he gains 20% of profit. His gain or loss percentage in the entire transaction is?Â [SSC – CGL – 2012]

A) 2% lossÂ Â Â Â Â Â Â Â Â Â B) 2% gainÂ Â Â Â Â Â Â Â Â Â Â Â Â Â C) 4% gainÂ Â Â Â Â Â Â Â Â Â Â Â Â Â D) 4% loss

Ans: D) 4% loss

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