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.
Profit and Loss Basic Concepts
Let us begin with the terminology for this topic.
1. Profit: Profit is the extra money earned when the Selling Price (SP) is more than the Cost Price (CP).
2. Loss: Loss is the money lost when the Selling Price (SP) is less than the Cost Price (CP).
3. Cost Price (CP): The amount paid to purchase an item.
4. Selling Price (SP): The amount received from selling an item.
5. Marked Price (MP): Original listed price before discounts.
6. Discount: A reduction applied to the original or marked price of a product or service.
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 |
Shortcut Method for Profit and Loss Calculation
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: Implify 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.
Profit and Loss Examples
Example 1: A person purchases a notebook from a supplier at Rs. 12 for 30 notebooks. He sells those notebooks at Rs. 15 for 20 notebooks. Find his profit or loss percent.
Solution:
Let’s find the cost price (CP) and selling price (SP) for each notebook.
CP for each notebook = 12/30 = Rs.0.40
SP for each notebook = 15/20 = Rs.0.75
Profit = SP – CP = Rs.0.75 − Rs.0.40 = Rs.0.35
Therefore, profit percent =
(0.35/0.40) × 100 = 87.5%
Example 2: A retailer offers two successive discounts of 15% and 25% on a line of shoes. Additionally, he provides a 10% discount for members. If a customer purchases a pair of shoes and is a member, what will be the overall discount percent applied to the shoes?
Solution:
Let the marked price (MP) of the shoes be Rs. 1000.
Calculate the first discount:
- First discount = 15% of MP = 15% × 1000 = Rs.150
- Price after first discount = 1000 − 150 = Rs.850
Calculate the second discount:
- Second discount = 25% of the new price = 25% × 850 = Rs.212.50
- Price after second discount = 850 − 212.50 = Rs.637.50
Calculate the member discount:
- Member discount = 10% of the new price = 10% × 637.50 = Rs.63.75
- Final price after member discount = 637.50 − 63.75 = Rs.573.75
Calculate the overall discount:
- Total discount = Marked Price - Final Price = 1000 − 573.75 = Rs.426.25
Calculate the overall discount percent:
- Overall Discount Percent = (426.25 / 1000) × 100 = 42.625%
Therefore, the overall discount percent on the shoes is 42.63%.
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