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
1. What is meant by the average cost price in Mathematics?
The average cost price is the mean value obtained by dividing the total cost price of all items by the number of items. This concept helps in determining the overall cost per unit when buying multiple items at different prices.
2. How can you calculate average cost price when the cost prices are different for each item?
To calculate the average cost price when cost prices vary, follow these steps:
- Add the cost prices of all items together.
- Count the total number of items purchased.
- Divide the total cost by the total number of items.
Formula: Average Cost Price = (Sum of all cost prices) / (Total number of items)
3. Why is understanding average cost price important for solving board-level Maths questions?
Understanding average cost price is crucial for solving board-level Maths questions because it enables students to tackle real-life applications related to profit and loss, and helps in answering word problems accurately as per the CBSE 2025–26 Maths syllabus.
4. What is the relation between cost price, selling price, and average cost price in profit questions?
In profit questions, the cost price is what is paid to acquire an item, the selling price is the price at which it is sold, and the average cost price is used if multiple items have different costs. To make a profit, the selling price of each item must be higher than the average cost price of all items.
5. How can mistakes occur while calculating the average cost price in exams?
Mistakes can occur if students:
- Do not add all the correct cost prices.
- Forget to count each item, especially if quantities differ.
- Divide by the wrong number (e.g., number of different types rather than total items).
Careful reading of the question and step-wise calculation prevent mistakes in average cost price problems.
6. How would you approach a complex question where items are bought at different prices and in varied quantities?
For such questions:
- Multiply the cost price of each group by the number of items in that group to get the total cost per group.
- Add all group totals to get the overall total cost.
- Add all item quantities to find the total number of items.
- Apply the formula: Average Cost Price = Total Cost / Total Number of Items.
7. What is the difference between Average Cost Price and Weighted Average Cost Price?
The Average Cost Price is used when all items are equally weighted. Weighted Average Cost Price is used when items are bought in different quantities, assigning proportional weight to each group based on quantity. In most CBSE board questions, the weighted method is used when quantities differ.
8. How does understanding average cost price help in real-life decision making?
Understanding average cost price is useful in real life for activities such as buying bulk items, comparing price advantages, managing inventory, and setting a selling price to ensure profitability.
9. What are common traps in average cost price questions in CBSE board exams?
Common traps include:
- Mixing up cost price and selling price.
- Ignoring items bought at different times or quantities.
- Incorrectly distributing profits or losses over all items rather than using the average.
10. Can the average cost price ever be equal to the selling price, and what does this imply?
If the average cost price equals the selling price, this means that there is neither profit nor loss on the overall transaction. For exam questions, this scenario typically represents a break-even point and is important for understanding profit calculations.
