Profit and loss are crucial topics in the Quantitative Aptitude sections of various competitive exams. To succeed in these exams, candidates must have a solid understanding of the cost price (CP) and selling price (SP) formulas, as well as the different types of profit and loss questions.
Basic Concepts
Let us begin with the terminology for this topic.
- Profit: Profit is the extra money earned when the Selling Price (SP) is more than the Cost Price (CP).
- Loss: Loss is the money lost when the Selling Price (SP) is less than the Cost Price (CP).
- Cost Price (CP): The amount paid to purchase an item.
- Selling Price (SP): The amount received from selling an item.
- Marked Price (MP): Original listed price before discounts.
- Discount: A reduction applied to the original or marked price of a product or service.
Formulas
Profit and loss is a topic that is asked in every placement exam. While the questions are not too tricky, some require a deeper understanding of concepts, but most of them are based on certain well-known formulas.
Name | Formulas |
Profit | Profit = Selling Price – Cost Price; (SP > CP) |
Loss | Loss = Cost Price – Selling Price; (CP > SP) |
Profit Percentage | Profit% = (Profit / Cost Price) x 100; (SP > CP) |
Loss Percentage | Loss% = (Loss / Cost Price) x 100; (CP > SP) |
Selling Price with Profit% | Selling Price = [(100 + Profit%) / 100] x Cost Price; (SP > CP) |
Selling Price (SP) with Loss % | Selling Price = [(100 - Loss%) / 100] x Cost Price; (SP < CP) |
Cost Price with Profit% | Cost Price = [100 / (100 + Profit%)] x Selling Price; (SP > CP) |
Cost Price (CP) with Loss% | Cost Price = [100 / (100 - Loss%)] x Selling Price; (CP > SP) |
Discount | Discount = Marked Price – Selling Price |
Relationship Between SP and CP
The relationship between cost price and selling price determines whether there is a profit or loss.
SP > CP : There is a profit.
SP = CP + Profit
SP < CP : There is a loss.
SP = CP − Loss
SP = CP There is neither profit nor loss.
SP = CP
Shortcut Methods
For easy calculation, we can use the below method:
The above image demonstrates a shortcut method to calculate the profit percentage based on the Cost Price (CP) and Selling Price (SP). Here’s how it works in simple steps:
Example 1:
Step 1: Write the ratio of CP to SP.
Calculate
\frac{\text{CP}}{\text{SP}} using the given values.Step 2: Simplify the ratio.
Reduce the fraction
\frac{\text{CP}}{\text{SP}} to its lowest terms, say ab\frac{a}{b} , where a and b are integers with no common factors.Step 3: Calculate the profit percentage.
Use the formula:P\% = \left( \frac{b - a}{a} \right) \times 100
- b - a is the profit in simplified units.
- Since CP is a units, divide the profit by a and multiply by 100 to get the percentage.
Example 2:
Step 1: Write the ratio of CP to SP and SP to MP.
- Calculate
\frac{\text{CP}}{\text{SP}} using the given values.- Calculate
\frac{\text{SP}}{\text{MP}} using the given values.Step 2: Simplify the ratio.
Reduce the fraction
\frac{\text{CP}}{\text{SP}} to its lowest terms, say ab\frac{a}{b} , where a and b are integers with no common factors and similar for SP and MP.Step 3: Adjust CP and MP so that SP has a Common Base.
Adjust the ratio to a common base using SP.
Multiply CP and MP by a factor to align with SP.
This step ensures consistency, but the simplified ratio (CP:SP) is used for calculation.
Step 4: Calculate the profit percentage.
Similar as shown in above example.
Properties
- Profit occurs when SP > CP.
- Loss occurs when SP < CP.
- There is no profit or loss when SP = CP
- Profit percentage is always calculated using cost price as the base.
- Loss percentage is also calculated using cost price as the base.
- Discount percentage is calculated using marked price as the base.
- Profit and loss are monetary differences between selling price and cost price.
- A discount reduces the marked price to obtain the selling price.
Applications
1. Business and Trading: Shopkeepers use profit and loss calculations to determine how much they earn or lose when selling goods.
2. Retail Shopping : Customers can calculate the actual selling price after discounts and determine whether an offer is beneficial.
3. Wholesale Transactions : Businesses compare purchasing and selling prices to determine their profit margins.
4. Discounts and Sales: Profit and loss calculations help businesses decide how much discount they can offer while maintaining a desired profit.
