👁 Preview — Study, Practice and Revise are open; mock tests and the rest of the syllabus unlock on subscription. Unlock all · ₹4,999
← Back to Arithmetic
Study mode

Commission

Study Practice Revise 🔒 Test

Commission

Commission is a fundamental concept in business and sales, where a person (called an agent or salesperson) earns a reward for selling goods or services. It is commonly expressed as a percentage of the sales value. This system motivates agents to maximize sales because a higher sale means a higher commission.

Typically, commission is calculated as a percentage of the sales amount or sometimes the cost price. Understanding how to calculate commission accurately is crucial, especially for exams and real-life business transactions.

Common terms to know:

  • Principal / Sales Amount: The total value of goods or services sold (in INR).
  • Commission Rate: The percentage rate at which the commission is paid.
  • Commission Amount: The actual money earned as commission.

Where is commission applied?

In real life, commission is paid to real estate agents, insurance agents, salespersons in shops, distributors, and many other professionals involved in selling products. This makes commission calculations highly practical and commonly tested for entrance exams.

Key Concept

Commission

A percentage reward given to a salesperson based on sales amount or profit earned.

Definition and Basic Formula

The basic formula to calculate commission is:

Basic Commission Formula

\[Commission = \frac{Commission\ Rate \times Sales\ Amount}{100}\]

Compute commission based on sales amount and rate.

Commission Rate = Percentage rate of commission
Sales Amount = Total sales value in INR

Here, the commission rate is always expressed as a percentage. By multiplying the sales amount by the commission rate and dividing by 100, you get the commission amount in INR.

Example to connect the idea:

Suppose an agent sells goods worth Rs.50,000 and earns a commission of 5% on sales. Then:

\( \text{Commission} = \frac{5 \times 50,000}{100} = Rs.2,500 \)

Sales Amount Commission Rate (%) Commission Amount x

Commission with Profit and Loss

Sometimes commission is based not on the total sales amount but rather on the profit earned or on the cost price or selling price of goods. This changes the calculation slightly and needs careful understanding.

Key points:

  • Cost Price (CP): The price at which the item was bought.
  • Selling Price (SP): The price at which the item was sold.
  • Profit or Loss = SP - CP: Positive value indicates profit, negative indicates loss.
  • Commission can be calculated on CP or SP depending on the agreement.

Formulas to remember:

Commission Type Formula When to Use
Commission on Cost Price \( \text{Commission} = \frac{\text{Commission Rate} \times \text{Cost Price}}{100} \) When commission is based on purchase price
Commission on Selling Price \( \text{Commission} = \frac{\text{Commission Rate} \times \text{Selling Price}}{100} \) When commission is based on sale price
Commission on Profit \( \text{Commission} = \frac{\text{Commission Rate} \times (\text{SP} - \text{CP})}{100} \) When commission is only on profit made

Commission Basis Comparison

  • Commission may be on cost price, selling price or profit
  • Know the basis before applying the formula
  • Profit = Selling Price - Cost Price (if positive)

Worked Examples

Example 1: Calculate simple commission Easy
Calculate the commission for an agent who sold goods worth Rs.50,000 at a 5% commission rate.

Step 1: Identify the sales amount and commission rate.

Sales amount = Rs.50,000, Commission rate = 5%

Step 2: Apply the basic commission formula:

\( \text{Commission} = \frac{5 \times 50,000}{100} \)

Step 3: Calculate:

\( = \frac{250,000}{100} = Rs.2,500 \)

Answer: The agent earns Rs.2,500 as commission.

Example 2: Commission on profit Medium
An agent receives 10% commission on the profit made by selling an item. The cost price is Rs.20,000, and the selling price is Rs.25,000. Calculate the commission.

Step 1: Calculate the profit.

Profit = Selling Price - Cost Price = Rs.25,000 - Rs.20,000 = Rs.5,000

Step 2: Commission rate is 10% on profit.

Commission = \( \frac{10 \times 5,000}{100} = Rs.500 \)

Answer: The agent's commission is Rs.500.

Example 3: Multiple transactions commission Medium
An agent makes two sales: Rs.30,000 at 4% commission and Rs.50,000 at 6% commission. Find the total commission earned.

Step 1: Calculate commission from first sale:

\( \frac{4 \times 30,000}{100} = Rs.1,200 \)

Step 2: Calculate commission from second sale:

\( \frac{6 \times 50,000}{100} = Rs.3,000 \)

Step 3: Add both to find total commission:

Rs.1,200 + Rs.3,000 = Rs.4,200

Answer: Total commission earned is Rs.4,200.

Example 4: Commission with discounts and profit Hard
An agent gets 7% commission on the selling price after giving a 10% discount on the marked price of Rs.60,000. If the cost price is Rs.45,000, calculate the commission.

Step 1: Find the selling price after discount.

Discount = 10% of Rs.60,000 = \( \frac{10 \times 60,000}{100} = Rs.6,000 \)

Selling Price = Marked Price - Discount = Rs.60,000 - Rs.6,000 = Rs.54,000

Step 2: Calculate commission (7% of selling price):

\( \frac{7 \times 54,000}{100} = Rs.3,780 \)

Answer: The agent receives Rs.3,780 as commission.

Example 5: Find commission rate Hard
An agent received Rs.1,200 as commission on sales of Rs.40,000. Find the commission rate.

Step 1: Use the basic commission formula:

\( \text{Commission} = \frac{\text{Commission Rate} \times \text{Sales Amount}}{100} \)

Step 2: Substitute known values to find commission rate:

\( 1,200 = \frac{\text{Commission Rate} \times 40,000}{100} \)

Step 3: Multiply both sides by 100:

\( 1,200 \times 100 = \text{Commission Rate} \times 40,000 \)

\( 1,20,000 = \text{Commission Rate} \times 40,000 \)

Step 4: Divide both sides by 40,000:

\( \text{Commission Rate} = \frac{1,20,000}{40,000} = 3\% \)

Answer: Commission rate is 3%.

Formula Bank

Basic Commission Formula
\[ \text{Commission} = \frac{\text{Commission Rate} \times \text{Sales Amount}}{100} \]
where: Commission Rate = percentage rate of commission, Sales Amount = total sales in INR
Commission on Cost Price
\[ \text{Commission} = \frac{\text{Commission Rate} \times \text{Cost Price}}{100} \]
where: Cost Price = price paid for the item, Commission Rate as a percentage
Commission on Selling Price
\[ \text{Commission} = \frac{\text{Commission Rate} \times \text{Selling Price}}{100} \]
where: Selling Price = price at which goods are sold, Commission Rate as a percentage
Profit and Loss
\[ \text{Profit or Loss} = \text{Selling Price} - \text{Cost Price} \]
where: Selling Price and Cost Price in INR

Tips & Tricks

Tip: Always check whether commission is on cost price or selling price.

When to use: When the problem states commission without specifying, or when profit/loss is involved

Tip: Use reverse calculation to find commission rate or sales amount.

When to use: When commission and one other variable are given, and you need to find missing data

Tip: Convert percentages to decimals for faster mental math.

When to use: During timed exams to save calculation time

Tip: Sum commissions separately for multiple transactions then add up.

When to use: For problems involving multiple commission rates or transactions

Common Mistakes to Avoid

❌ Assuming commission is always on selling price.
✓ Read problem carefully and identify whether commission is on cost price or selling price.
Why: Different bases affect calculation significantly.
❌ Confusing commission rate percentage with profit percentage.
✓ Separate commission calculation from profit/loss calculation distinctly.
Why: Commission and profit are related but different entities.
❌ Forgetting to convert percentages into decimal form during calculations.
✓ Always divide percentage by 100 or convert to decimal before multiplying.
Why: Prevents incorrect commission amount.
❌ Mixing up units or currency (e.g., using non-INR values).
✓ Use consistent units (INR) throughout and verify values.
Why: Ensures clarity and correctness in calculations.
Curated videos per subtopic
Top YouTube explainers, AI-ranked for your exam and language. Unlocks with subscription.
Unlock

Try Practice next.

Progress tracking is paywalled — subscribe to mark subtopics as understood and save your streak.

Go to practice →
Ask a doubt
Commission · 10 free messages
Ask me anything about this subtopic. You have 10 free messages this session — chat history isn't saved in preview.