The percentage is one of the most important topics which is the backbone of calculations that is either incorporated in commercial arithmetic or in real life. Involving the concept of percentages in the profit and loss concept, it becomes very important to know the clear concepts of percentages that will help you solve all the questions in a fraction of seconds without the need for pen or paper.

Besides this, 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 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.

### What are Profit and Loss?

Let us suppose that Neha purchased an advanced model of Fastrack watch from Flipkart’s exclusive product Diwali sale at Rs. 1200. After a few days, she got bored with the model and decided to sell it to someone at Rs. 1350. Now, what do you think she incurred a loss or gained a profit.

Here, we noticed that the C.P. or the cost price at Flipkart is Rs. 1200. Now, the S.P. or the selling price of the same watch becomes Rs. 1350. Now, let us find the difference in the current price and the previous price, which is: 1350 - 1200 = 150.

So, here, Neha still has Rs. 150 with her even after selling her product, which means she gained a profit.

On the other hand, if the product was already purchased by many people on the same date and the value of the watch depreciated to Rs. 1150, then the current price or the S.P. becomes Rs. 1150, whose the previous price or C.P. was Rs. 1200.

So, Neha could not receive any money even after selling the watch, i.e., she incurred a loss of Rs. 50 (1150 - 1200).

This is how we understand the concept of profit and gain in real life. Now, let us merge this concept of Loss with percentages. There is a high demand of this combinational concept, as many questions come in the exam.

### Loss Percentage Formula in Maths

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) %.

### Other Important Loss and Profit Percentage Formulas in Maths

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 the 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.

Discount = M.P. - S.P.

Discount % = (Discount/Marked Price) 100

Therefore, the mentioned 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.

Loss % or L% = (L/CP) x 100

When the product is sold at Rs. x and the profit is m % and if the loss is n %, then the net % profit or loss will be: (m - n - mn)/100.

Suppose the dinner set of 35 pieces is sold at m % profit and then again sold at n% profit the actual cost price of the dinner set will be:

In case of proCP = \[100 \times 100 \times \frac{P}{(100 + m)(100 + n)}\].

However, in the case of loss, CP = \[100 \times 100 \times \frac{P}{(100 - m)(100 - n)}\]

If P% and L% of the product sold are equal then, P = L and % \[loss = \frac{P^{2}}{100}\].

### Quiz Time

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:

650

720

600

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 the 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 percent.

Options:

10%

2%

3%

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.

### Solved Examples

Example 1: A shopkeeper of electronic goods incurred a loss in a deal that is 3/5th of the selling price. Find out the loss percent.

Solution

Let the SP of the good be x

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

Using the formula for loss percentage equation: Loss % = \[\left ( \frac{Loss}{Cost Price} \right ) \times 100\]

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

Loss.

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

### Conclusion

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.