Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Cost Price (CP): The price at which an item is purchased by a shopkeeper or person. Think of it as the starting amount of money spent. In a diagram, you can visualize CP as the base level of an investment.
Selling Price (SP): The price at which an item is sold to a buyer. If you look at a price tag in a store, that amount represents the SP. On a number line, if SP is to the right of CP, it indicates a gain.
Profit (Gain): When the Selling Price is greater than the Cost Price (), the difference is called Profit. Imagine a bar chart where the SP bar is taller than the CP bar; the extra height on the SP bar represents the profit earned.
Loss: When the Selling Price is less than the Cost Price (), the difference is called Loss. Visually, if the CP bar is taller than the SP bar, the missing section needed for SP to reach CP represents the loss.
Overhead Charges: These are additional expenses like transportation, labor, or repair costs incurred after buying an item. To find the 'Total Cost Price', you must add these overheads to the original CP. Imagine a large box labeled 'Total CP' which contains the 'Buying Price' plus several smaller boxes of 'extra costs'.
Profit and Loss Percentage: This is the calculation of profit or loss relative to the Cost Price, expressed as a fraction of 100. You can visualize this as a pie chart where the total Cost Price is the whole circle, and the profit or loss is a slice of that circle.
No Profit No Loss: If the Selling Price is exactly equal to the Cost Price (), there is no profit and no loss. On a scale, this represents a perfect balance where neither side is heavier.
📐Formulae
💡Examples
Problem 1:
A shopkeeper bought a bicycle for and spent on its repairs. He then sold it for . Calculate his profit or loss percentage.
Solution:
- Find Total Cost Price: Original , Overheads = . Total . \ 2. Identify SP: . \ 3. Compare SP and CP: Since (), it is a Profit. \ 4. Calculate Profit: . \ 5. Calculate Profit Percentage: .
Explanation:
First, we calculate the Total Cost Price by adding the repair costs to the buying price. Since the selling price is higher than the total cost price, we calculate the profit and then convert it into a percentage relative to the total cost price.
Problem 2:
Ramesh bought 100 oranges for . Out of these, 10 oranges were rotten and could not be sold. He sold the remaining oranges at each. Find his profit or loss.
Solution:
- Cost Price: . \ 2. Remaining Oranges: Total oranges = . Rotten oranges = . Salable oranges = . \ 3. Total Selling Price: . \ 4. Compare CP and SP: Since (), it is a Loss. \ 5. Calculate Loss: .
Explanation:
We first identify the total amount spent. Then, we find out how many oranges are actually available to be sold by subtracting the rotten ones. By multiplying the number of good oranges by the rate, we find the total selling price. Comparing this to the cost price reveals a loss.