How to Use the Cost Price Formula with Solved Examples
The cost price formula, which is also known as CP, is used to determine an item's actual price. In other words, it is the cost of any commodity that we buy. Through the selling price, the cost price aids in determining profitability.
Cost Price Formula
As a result, you make a profit if the original value is less than the selling price, and you lose money if the original value is higher than the selling price. In order to better understand this, we will discuss two cost price formulas in this section, understand the variables at play, and work through a few examples.
Definition of Cost Price:
Person Buying Books
The cost price is the sum of money used to produce goods or services before any profit is added for the manufacturer or producer. Other names for it include last cost, average cost, and actual cost.
The extra costs associated with production, real estate, materials, electricity, R&D, testing, worker wages, and other expenses are all included in the cost price. The cost price and the selling price of any item are always used to determine profit and loss.
Cost Price and Selling Price:
Cost Price and Selling Price
Cost Price: The cost price of an item is the sum paid to obtain it or the cost at which it was produced. The cost price is denoted by the letter C.P.
Selling Price: The selling price is the cost at which an item is offered for sale. The selling price is denoted by the letter S.P.
How Do You Evaluate Cost Price?
Evaluating Cost Price
By comparing the profit to the selling price, the CP is used to confirm the profit. This implies that there is a profit in the purchase if the original value, which is the C.P., is lower than the selling price. Additionally, the purchase will result in a loss if the C.P. is higher than the S.P.
What is the Cost Price Formula?
Formulas
Let’s learn the cost price formula in math from the following-
To determine whether we made money when we sold a product, we used the formula below.
The Formula for Cost Price (CP) : Selling Price (SP) - Profit
We use the following formula if we lose money while selling a product.
The Formula for Cost Price (CP) : Selling Price (SP) + Loss
The following is the formula for profit (gain) percentage and selling price
The Formula for Cost Price(CP) : {100/(100 + Profit %)} x SP.
The equation based on loss percentage and SP is as follows
The Formula for Cost Price(CP) : {100/(100 - Loss %)} x SP
Solved Examples:
Learning From Examples
1. On selling a chair for Rs500, James loses 6%. For how much did she purchase it? Calculate the cost price by using the formula.
Ans: Given, Loss = 6%; SP = Rs 500; CP = ?
If the loss is 6%, it means that if the cost price is Rs100, the loss incurred is Rs6.
If CP is Rs. 100, then SP is Rs. 94
When SP is Rs. 94, CP = Rs. 100
When SP is Rs. 500
CP = (100/94) × 500 = Rs531.90
∴ CP = Rs. 531.90
Therefore, the cost price of the chair is Rs. 531.90
2. If by selling a particular test series at Rs. 300 a website earns a profit of Rs. 46. then determine the CP of the test series.
Ans: Here is the selling price of the test series=Rs. 330 and profit = Rs. 46
Using the formula, we get:
CP = Selling Price - Profit
= 300-46
CP of the test series = Rs.254
Let’s Practise:
Practice Time
The selling price of a toy is Rs. 340 and the profit earned by the shopkeeper is Rs. 60. Find the cost price of the toy using the cost price formula.
Ans: Rs. 280
An article was sold for Rs. 230 at a loss of Rs. 20. Using the cost price formula can you calculate what was its cost price?
Ans: Rs. 250
Summary
The original cost of making a product, along with some additional costs incurred during the manufacturing process, is the cost price of the product. Calculating the actual profit of the product, its manufacturer, and its developer is helped by differences between the selling price and cost price of the products.
FAQs on Cost Price Formula in Profit and Loss
1. What is the cost price formula?
The cost price formula is Cost Price (CP) = Selling Price (SP) − Profit or CP = SP + Loss, depending on whether there is profit or loss.
- If there is profit: CP = SP − Profit
- If there is loss: CP = SP + Loss
2. What is the formula for cost price when profit percentage is given?
The formula for cost price when profit percentage is given is CP = (SP × 100) / (100 + Profit%).
- Step 1: Note the Selling Price (SP).
- Step 2: Add 100 to the profit percentage.
- Step 3: Multiply SP by 100 and divide by (100 + Profit%).
3. What is the formula for cost price when loss percentage is given?
The formula for cost price when loss percentage is given is CP = (SP × 100) / (100 − Loss%).
- Step 1: Write the Selling Price (SP).
- Step 2: Subtract the loss percentage from 100.
- Step 3: Multiply SP by 100 and divide by (100 − Loss%).
4. How do you calculate cost price from selling price and profit?
You calculate cost price using CP = SP − Profit.
- Example: If SP = 500 and Profit = 80
- CP = 500 − 80 = 420
5. How do you calculate cost price from selling price and loss?
You calculate cost price using CP = SP + Loss.
- Example: If SP = 700 and Loss = 50
- CP = 700 + 50 = 750
6. What is the relationship between cost price, selling price, and profit?
The relationship is Profit = SP − CP and SP = CP + Profit.
- If SP > CP → Profit
- If SP < CP → Loss
7. Can you give an example of finding cost price using profit percentage?
Yes, cost price can be found using CP = (SP × 100) / (100 + Profit%).
- Example: SP = 660, Profit% = 10%
- CP = (660 × 100) / 110
- CP = 66000 / 110 = 600
8. What is the difference between cost price and selling price?
The cost price (CP) is the price at which an item is purchased, while the selling price (SP) is the price at which it is sold.
- If SP > CP → Profit
- If SP < CP → Loss
9. How do you find cost price when profit is 25% and selling price is 1000?
The cost price is found using CP = (SP × 100) / (100 + Profit%).
- CP = (1000 × 100) / 125
- CP = 100000 / 125 = 800
10. What are common mistakes to avoid when using the cost price formula?
Common mistakes include using the wrong formula and confusing profit percentage with selling price percentage.
- Profit% and Loss% are always calculated on Cost Price, not Selling Price.
- Use CP = SP − Profit only when profit value is given.
- Use percentage formulas carefully: (100 + Profit%) or (100 − Loss%).
