When goods are bought for one sum of money and sold for another, there is a profit and loss, depending on whether the selling price (SP) is greater or less than the cost price (CP), respectively. If the goods are bought and sold for the same sum of money, then there is no profit, no loss. Profit or loss is generally represented as a percent of the cost price unless otherwise stated.
To effectively tackle profit and loss problems in competitive exams, start by understanding key formulas related to profit, loss, and their respective percentages. Practice solving a variety of scenarios using these formulas, along with shortcuts and essential concepts like CP, SP, and the correlation between profit/loss and CP.
Fundamental Formulas
- Profit = Selling Price (SP) – Cost Price (CP)
- Loss = Cost Price (CP) – Selling Price (SP)
- Profit Percentage = (Profit / CP) × 100
- Loss Percentage = (Loss / CP) × 100
Selling Price and Cost Price Calculations
- Finding SP when Profit is given:
SP = (1 + Profit%/100) × CP - Finding SP when Loss is given:
SP = (1 – Loss%/100) × CP - Finding CP when Profit is given:
CP = SP/ (1 + Profit%/100) - Finding CP when Loss is given:
CP = SP/ (1 – Loss%/100)
Key Concepts to Understand
- Marked Price (MP): The price displayed before discounts apply.
- Discount: The reduction applied to MP to determine the final SP.
- Marked Price (MP) is the base price of a product before any discount is given. It is also known as the List Price. The mark-up is taken on the Cost Price (CP). Thus, MP = CP+ Mark-up
- Discount is calculated over MP
- Discount = Marked Price (MP) – Selling Price (SP)
- Discount% = (Discount/MP) × 100
- Break-Even Point: The stage where total revenue equals total cost, resulting in neither profit nor loss.
Steps to Solve Profit and Loss Questions Effectively
- Analyze the given information: Identify the known values (CP, SP, profit%, loss%) and determine what needs to be calculated.
- Select the appropriate formula: Choose the correct equation based on the provided data.
- Plug in the values: Substitute the known figures into the selected formula.
- Compute and verify: Perform the necessary calculations and cross-check your answer for accuracy and logical consistency.
By mastering these concepts and practicing regularly, you can significantly improve your problem-solving speed and accuracy in profit and loss problems .
To understand the application of the concepts explained above, you may access the following links:
