Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Cost Price (CP) and Selling Price (SP): The Cost Price is the total amount paid to buy an article, including any overhead expenses like transportation or repairs. Visualize the CP as the starting point of a transaction. The Selling Price is the amount at which the article is sold to a customer. Imagine a bar chart where CP is the base bar and SP is the bar that follows it.
Profit and Loss: Profit occurs when the Selling Price is greater than the Cost Price (), which can be visualized as an upward-pointing green arrow indicating growth. Loss occurs when the Cost Price is greater than the Selling Price (), visualized as a downward-pointing red arrow indicating a deficit.
Profit and Loss Percentage: These are the gains or losses expressed as a fraction of 100, always calculated on the Cost Price unless specified. Visualize this as a pie chart where the CP is the whole, and the profit or loss is a slice whose size relative to the whole determines the percentage.
Marked Price (MP) and Discount: The Marked Price (also known as the List Price) is the price printed on the label of an item. A Discount is a reduction offered on the Marked Price to attract customers. Visualize a price tag where the original price is crossed out and a lower price is written below it.
Net Selling Price after Discount: The actual price a customer pays after the discount is subtracted from the Marked Price. In a visual flow, this is the result of starting at the MP and moving 'downwards' by the discount amount to reach the SP.
Successive Discounts: This involves applying more than one discount consecutively. The first discount is applied to the Marked Price, and the second discount is applied to the reduced price obtained after the first discount. Visualize this as a staircase where the price drops at each step, rather than one single large drop.
Overhead Expenses: These are additional costs like rent, labor, or freight incurred before selling. These are always added to the original purchase price to calculate the 'Effective Cost Price'. Imagine adding smaller blocks of cost on top of the initial purchase block to get the total height of the CP bar.
Tax (GST/VAT): Tax is an extra amount charged by the government on the selling price of an item. It increases the final amount to be paid by the customer. Visualize a billing receipt where the 'Subtotal' is the SP, and the 'Grand Total' is higher because the tax amount is added to it.
📐Formulae
SP = \\frac{100 + Profit \\%}{100} \\times CP
SP = \\frac{100 - Loss \\%}{100} \\times CP
CP = \\frac{100}{100 + Profit \\%} \\times SP
CP = \\frac{100}{100 - Loss \\%} \\times SP
SP = MP \\times (1 - \\frac{Discount \\%}{100})
💡Examples
Problem 1:
A shopkeeper bought a refrigerator for ₹15,000 and spent ₹1,000 on its transportation. He then sold it for ₹18,400. Calculate his profit or loss percentage.
Solution:
- Find Total Cost Price:
- Identify SP:
- Compare SP and CP: Since , it is a Profit.
- Calculate Profit:
- Calculate Profit Percentage:
Explanation:
First, the overhead costs are added to the purchase price to find the effective CP. Then, the difference between SP and CP gives the profit, which is then divided by the CP and multiplied by 100 to find the percentage.
Problem 2:
A dining table is marked at ₹5,000. The shopkeeper offers a discount of 10% and then a further seasonal discount of 5%. Find the final selling price of the table.
Solution:
- Apply first discount on Marked Price: ,
- Price after first discount:
- Apply second discount on the reduced price: ,
- Final Selling Price (): Alternative method:
Explanation:
This problem demonstrates successive discounts. The key is to apply the second discount to the price remaining after the first discount, not the original marked price.