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Calculating the Percentage loss or gain is a crucial concept. Many financial, statistical as well as real life examples are near or far related to the concept of Percentage loss. To evaluate the percentage gain or loss on an investment, buyers need to first ascertain the purchase price and for that we use the loss and profit percentage formula. Using the formula, you will also learn of how to represent the loss in the form of a percentage. In this chapter we are going to cover the important descriptions, formulas, solved examples and wrap it up with some quiz questions.

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We incur a loss when the selling price of an article is less than the cost price. Thus when (SP) < (CP) then there is a loss. The formula to calculate the amount of loss is

Loss = {(Cost Price) {C.P} - {(Selling Price) {S.P}

Loss % = (loss/ CP × 100) %.

Basic Terms and Formulas

Cost price (C.P.): Price at which an item is purchased.

Selling price (S.P.): Price at which an item is sold.

Profit or Gain: When selling price is higher than the cost price, and the difference between them is the profit gained.

Formula: Profit = S.P. – C.P.

Loss: When the cost price is higher than the selling price, and the difference between them is the loss suffered.

Formula: Loss = C.P. – S.P.

Remember: Loss or Profit is always computed on the cost price.

Marked Price/List Price: price at which the selling price on an article is marked

Discount: price offered as a discount, concession or rebate on the marked price.

Profit% = [Profit / CP] × 100

Loss % = [Loss / CP] × 100

The aforementioned two formulas can be described as,

If an item is sold at a profit of 25%, then SP = 125% of CP.

If an item is sold at a loss of 25%, then SP = 75% of CP.

\[Gain% = \frac{Gain \times 100}{CP}\]

\[Loss% = \frac{Loss \times 100}{CP}\]

\[C.P. = (\frac{100}{100 + Gain}) \times S.P\]

\[S.P. = (\frac{100 + Gain%}{100}) \times C.P\]

\[S.P. = (\frac{100 - Loss%}{100}) \times C.P\]

\[C.P. = (\frac{100%}{100 - Loss%) \times S.P\]

Profit and Loss problems are not restricted to just elementary studies but are beneficial for life long and are even directly relevant for competitive entrance exams (like CAT, GMAT, GRE, IBPS, UPSC). Problems based on loss and profit percentage formula are also pertinent for the MBA syllabus like Financial Statements, stock market, trading, accounting, and more.

1. After giving successive discounts of 10% and 5% on a pair of shoes, it was sold at Rs. 513. Tell us the list price of the shoes.

Options:

A. 650

B.720

C.600

D.528

Solution:

\[\frac{90}{100} \times \frac{95}{100} \times x = 513\]

x = Rs. 600

Hence, the answer is option C. as the list price of shoes, i.e. before discount is Rs. 600.

2. Jessica bought a bicycle for Rs. 1300. She also has to spend Rs. 70 on its repairs. Due to its some issue, she had to sell it for 1185. Find her loss per cent.

Options:

A. 10%

B.2%

C.3%

D.13.50%

Solution:

CP = Rs.1300 + 70 = 1370 and SP = Rs 1185.

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

Loss = Rs. (1370 - 1185)

= Rs. 185

Loss % = \[(\frac{185}{1370}) \times 100 %\]

= 13.50%

Hence, the answer is option D.

Example1:

The cost price of 20 notebooks is similar to the selling price of ‘n’ number of notebooks. The seller incurred a loss of 40%. Find out the value of n?

Solution1:

Let the price of each notebook be Re. 1.

Then the CP of n notebooks is Rs. n and the SP of n notebooks is Rs. 10.

Loss = n - 10

\[Loss % = (\frac{loss}{CP}) \times 100 = 40\].

Thus, \[\text{loss of } 40% = [\frac{n - 10}{n}] \times 100 = 40\].

Hence the value of n → 17 (approx).

Example2:

A shopkeeper of electronic goods incurred a loss in a deal that is 3/5th of the selling price. Find out the loss percent.

Solution2:

Let the SP of the good be x

\[Loss = \frac{3x}{5}\]

Using the formula for loss percentage equation: Loss % = (Loss / Cost Price) × 100

\[CP = SP + loss = x + \frac{3x}{5} = \frac{8x}{5}\].

\[Loss% = \frac{(\frac{3x}{5})}{(\frac{8x}{5}) \times 100 = 37.5%\].

Hence, the loss % incurred by the shopkeeper is 37.5%.

FAQ (Frequently Asked Questions)

Q1. Is the Cost Price of an Item the Price that we Pay at the Time of Purchase to the Seller?

Ans. Generally, the cost price of an item is the price paid to acquire that item. However when calculating percent of profit percent and loss, we also have to add the extra cost incurred on that item. For example, sometimes after purchasing an item, we have to spend additional money over things like transportation, local taxes, repairing, modifying etc. These extra expenses add to the cost price and are called overheads. Thus, to calculate the total cost price, we add overheads and additional costs to the purchase price.

Q2. How is Percentage Loss and Profit Relevant to Business?

Ans. Profit and loss is not only significant branch mathematics but it also deals with the real time profit and loss made in a business transaction. The profit and loss statement is critically a summary of the trading transactions and reveals whether a business has made a profit or loss during a specified frame of account. As a matter of fact, deducting the total expenditure from total income, we can calculate the profit or loss of a business. Together with the balance sheet, it is one of the pivotal financial statements that make up a company’s statutory accounts. Basically, a loss and profit percentage account reveals the following information for a business:

Cost of sales.

Operating costs incurred by the business.

Sales revenue.

Profit/Loss earned by a business.