How to Calculate Average Cost Price with Formula and Solved Examples
We know that when we buy a product, we have to pay for it. Actually, we buy goods and products at their selling prices or the MRP. But what about the shopkeeper? Does he get any profit from selling goods to us?
Of course, he gets his profit amount for selling goods.
So, what is the actual cost price of the goods? How much a shopkeeper earns on each product and how to calculate average cost price.
When there are many products to be bought and sold, we use the concept of average cost price. Also, mathematics has given us an average cost price and average cost formula to make the buying and selling process easier.
Cost Price and Selling Price
The amount that is spent by the manufacturer to produce goods or services before any profit is added for the producer or the amount at which a good is bought/purchased before selling it to the customer is called cost price. Cost price is also known as CP. It is the original price of any product. The price at which a good is finally sold to us is called its selling price.
How to Find the Cost Price?
Consider the situation given below.
Suppose your friend gives you ₹20 for a pen that you got for ₹15. Is it the actual cost of the pen?
No, it is not. In this case,₹15 was the cost price for you as it was the amount at which you bought the pen. But ₹20 will be the cost price for your friend, while that same amount of ₹20 will be your selling price. In this case, you are earning a profit of ₹5.
So, CP= SP- profit
If we reverse the situation and assume that you sold the pen to your friend at ₹10, then ₹10 becomes your SP and her CP. In this case, you are incurring a loss of 5.
So, CP=SP+ loss
Similarly, in the supply chain, somebody’s cost price is someone else’s selling price. The manufacturer actually pays the cost for the pen and gets a profit amount on selling it to the distributor.
The distributor also gets an amount of profit for selling it to the shopkeeper. After that, the shopkeeper also gets a profit from selling the pen to us at the MRP.
Average Cost Price and Average Cost Formula
The average cost price is the mean of all cost prices or the ratio of cost of all products to the number of products. In other words, it is the arithmetic average of the amount involved in producing the total number of items.
= (total cost of production divided by the number of units).
Suppose a shopkeeper combined a new stock of shoes with an old stock, and the new price overstates the value of the stock holding. There is a better method to combine the total cost price of both stocks.
The formula to calculate the average cost price is given below:
X = ∑(xi)/n
The symbol ∑, called sigma is used for the notation of summation.
xi is the sum of cost prices and n is the number of total items.
Examples of Average Cost Price
Problem 1:
A shopkeeper sells different types of shoes. He sells six shoes for the costs ₹700, ₹750, ₹800, ₹1000, ₹1100 and ₹1350. Find the average cost price of a shoe he sold.
Solution:
Number of shoes= 6
Average cost price X = ∑(xi)/n
X= (700+750+800+1000+1100+1350)/6
X= 5700/6
X= ₹950
Hence, the average cost price of shoes is ₹950.
Problem 2:
A shopkeeper has four plastic buckets in old stock for cost prices ₹100, ₹120, ₹130 and ₹150. He combines four new plastic buckets with the old stock for cost prices ₹140, ₹160, ₹175 and ₹185. Find the average cost price of the total stock? Also, find his net loss or gain if he sells each old bucket for ₹140 and each new bucket for ₹160.
Solution:
Total number of plastic buckets= old stock + new stock
=4+4= 8
Average cost price X = ∑(xi)/n
X= (100+120+130+150+140+160+175+185)/8
X= 1160/8
X= ₹145.
Hence, the average cost price of the total stock is ₹145.
Total SP of old buckets = ₹140x4= ₹560
Total SP of new buckets= ₹160x4= ₹640
Therefore, the total selling price is (560+640)= ₹1200.
Total cost price= ₹1160
This is a case of profit as SP> CP. The profit here is (1200-1160) = ₹40.
Did You Know?
When we calculate the net profit or loss percentage for any business transaction, it is always expressed in terms of the cost price.
Therefore, profit % = (profit/CP)x100 and loss %= (loss/CP)x100
FAQs on Average Cost Price in Maths with Formula and Steps
1. What is average cost price in maths?
The average cost price is the total cost of all items purchased divided by the total number of items. It is used when goods are bought at different prices and we want a single equivalent cost per unit.
- Formula: Average Cost Price = Total Cost ÷ Total Quantity
- It helps in calculating profit, loss, and selling price easily.
2. What is the formula for average cost price?
The formula for average cost price is Total Cost divided by Total Quantity.
- Average Cost Price = (Cost₁ + Cost₂ + …) ÷ (Quantity₁ + Quantity₂ + …)
- It applies when items are purchased at different rates.
3. How do you calculate average cost price with different quantities?
To calculate average cost price with different quantities, first find the total cost and then divide by the total number of units.
- Step 1: Multiply each quantity by its cost price.
- Step 2: Add all the costs to get total cost.
- Step 3: Add all quantities.
- Step 4: Divide total cost by total quantity.
4. What is the difference between cost price and average cost price?
The cost price is the price of a single item, while the average cost price is the combined cost per item when multiple items are bought at different prices.
- Cost Price (CP): Price at which one item is purchased.
- Average Cost Price: Total cost of all items ÷ Total number of items.
5. Can you give an example of average cost price?
An example of average cost price is when goods are bought at two different rates and combined into one stock.
- A shopkeeper buys 10 pens at ₹5 each and 20 pens at ₹8 each.
- Total cost = (10×5) + (20×8) = 50 + 160 = ₹210.
- Total quantity = 30 pens.
- Average cost price = 210 ÷ 30 = ₹7 per pen.
6. Why is average cost price important in profit and loss?
The average cost price is important in profit and loss because it gives a single cost value to calculate overall profit or loss accurately.
- Profit = Selling Price − Average Cost Price
- Loss = Average Cost Price − Selling Price
7. What happens to average cost price when more items are bought at a higher price?
The average cost price increases when more items are purchased at a higher price than the existing average.
- If new cost > current average → Average increases.
- If new cost < current average → Average decreases.
8. Is average cost price the same as weighted average?
Yes, the average cost price is calculated using the weighted average method when quantities differ.
- Each price is weighted by its quantity.
- Formula: Weighted Average = (Σ Quantity × Price) ÷ Σ Quantity.
9. How do you find the selling price using average cost price?
The selling price can be found by adding desired profit to the average cost price or subtracting loss from it.
- Selling Price = Average Cost Price + Profit
- Selling Price = Average Cost Price − Loss
10. What are common mistakes when calculating average cost price?
A common mistake in calculating average cost price is dividing by the number of price groups instead of the total quantity.
- Wrong: (Price₁ + Price₂) ÷ 2
- Correct: Total cost ÷ Total quantity
- Forgetting to multiply quantity by price.
