👁 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

Profit and Loss

Study Practice Revise 🔒 Test

Introduction to Profit and Loss

Imagine you buy a bicycle for Rs.5,000 and later sell it for Rs.6,000. You have made some money from this transaction. This money earned is called profit. On the other hand, if you sell the bicycle for Rs.4,500, you lose some money, which is called a loss.

In everyday life, buying and selling goods is common. Understanding profit and loss helps us know whether we are gaining or losing money in such transactions. This section will explain these concepts clearly, using simple examples and step-by-step calculations.

Basic Definitions and Relationships

Before we dive deeper, let's define some important terms:

  • Cost Price (CP): The price at which an item is bought.
  • Selling Price (SP): The price at which the item is sold.
  • Profit: When SP > CP, the difference is called profit.
  • Loss: When CP > SP, the difference is called loss.
Cost Price (CP) Selling Price (SP) Loss (SP < CP) Profit (SP > CP)

How to calculate profit or loss amount?

  • Profit = SP - CP, if SP > CP
  • Loss = CP - SP, if CP > SP

These formulas help us find the exact money gained or lost in a transaction.

Profit and Loss Percentage

Simply knowing the amount of profit or loss is not always enough. Sometimes, we want to know how much profit or loss was made relative to the cost price. This is where percentages come in handy.

Profit Percentage tells us what percent of the cost price is the profit. Similarly, Loss Percentage tells us what percent of the cost price is the loss.

Type Formula Explanation
Profit % \( \text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \) Profit as a percentage of cost price
Loss % \( \text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \) Loss as a percentage of cost price

Why calculate percentages? Because percentages allow easy comparison between different transactions, regardless of the absolute amounts involved.

Discounts and Marked Price

In shops, the price displayed on an item is often called the marked price or list price. Sometimes, sellers offer a reduction on this price, called a discount. The price after discount is the actual selling price.

Understanding discounts is important because they affect profit and loss calculations.

graph TD    MP[Marked Price]    MP -->|Apply Discount| D[Discount Amount]    D -->|Subtract| SP[Selling Price]

Here,

  • Discount = Marked Price - Selling Price
  • If discount is given in percentage, then
  • SP = Marked Price x (1 - Discount % / 100)

Worked Examples

Example 1: Basic Profit Calculation Easy
Calculate the profit when the cost price (CP) of an item is Rs.500 and the selling price (SP) is Rs.600.

Step 1: Identify CP and SP.

CP = Rs.500, SP = Rs.600

Step 2: Since SP > CP, there is a profit.

Step 3: Calculate profit using the formula:

\( \text{Profit} = SP - CP = 600 - 500 = Rs.100 \)

Answer: The profit is Rs.100.

Example 2: Profit Percentage Calculation Easy
Find the profit percentage if the cost price is Rs.800 and the selling price is Rs.920.

Step 1: Calculate profit amount.

\( \text{Profit} = SP - CP = 920 - 800 = Rs.120 \)

Step 2: Calculate profit percentage.

\( \text{Profit \%} = \left( \frac{120}{800} \right) \times 100 = 15\% \)

Answer: The profit percentage is 15%.

Example 3: Selling Price after Discount Medium
Calculate the selling price of an article if the marked price is Rs.1500 and a discount of 20% is given.

Step 1: Identify marked price (MP) and discount %.

MP = Rs.1500, Discount = 20%

Step 2: Calculate selling price using the formula:

\( SP = MP \times \left(1 - \frac{\text{Discount \%}}{100}\right) = 1500 \times (1 - 0.20) = 1500 \times 0.80 = Rs.1200 \)

Answer: The selling price after discount is Rs.1200.

Example 4: Successive Discounts Medium
Find the final price of an article with a marked price of Rs.2000 after successive discounts of 10% and 5%.

Step 1: Calculate price after first discount (10%).

\( \text{Price after first discount} = 2000 \times (1 - 0.10) = 2000 \times 0.90 = Rs.1800 \)

Step 2: Calculate price after second discount (5%) on the new price.

\( \text{Final price} = 1800 \times (1 - 0.05) = 1800 \times 0.95 = Rs.1710 \)

Answer: The final price after successive discounts is Rs.1710.

Example 5: Mixed Profit and Loss Hard
A shopkeeper gains 10% on one article and loses 10% on another article, both having the same cost price of Rs.1000 each. Find the overall gain or loss.

Step 1: Calculate selling price of first article with 10% gain.

\( SP_1 = CP \times \left(1 + \frac{10}{100}\right) = 1000 \times 1.10 = Rs.1100 \)

Step 2: Calculate selling price of second article with 10% loss.

\( SP_2 = CP \times \left(1 - \frac{10}{100}\right) = 1000 \times 0.90 = Rs.900 \)

Step 3: Calculate total cost price and total selling price.

Total CP = 1000 + 1000 = Rs.2000

Total SP = 1100 + 900 = Rs.2000

Step 4: Compare total SP and total CP.

Since total SP = total CP, there is neither overall gain nor loss.

Answer: The shopkeeper breaks even with no overall gain or loss.

Profit

Profit = SP - CP

Used when selling price is greater than cost price to find profit amount.

SP = Selling Price
CP = Cost Price

Loss

Loss = CP - SP

Used when cost price is greater than selling price to find loss amount.

CP = Cost Price
SP = Selling Price

Profit Percentage

\[\text{Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\]

Calculates profit as a percentage of cost price.

Profit = SP - CP
CP = Cost Price

Loss Percentage

\[\text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\]

Calculates loss as a percentage of cost price.

Loss = CP - SP
CP = Cost Price

Selling Price from Profit Percentage

\[SP = CP \times \left(1 + \frac{\text{Profit \%}}{100} \right)\]

Finds selling price when profit percentage is known.

CP = Cost Price

Selling Price from Loss Percentage

\[SP = CP \times \left(1 - \frac{\text{Loss \%}}{100} \right)\]

Finds selling price when loss percentage is known.

CP = Cost Price

Discount

\[Discount = \text{Marked Price} - \text{Selling Price}\]

Calculates discount amount given marked price and selling price.

Marked Price = Original price before discount

Selling Price after Discount

\[SP = \text{Marked Price} \times \left(1 - \frac{\text{Discount \%}}{100} \right)\]

Calculates selling price after applying discount percentage.

Marked Price = Original price
Discount % = Percentage discount

Successive Discounts

\[SP = \text{Marked Price} \times \left(1 - \frac{d_1}{100} \right) \times \left(1 - \frac{d_2}{100} \right) \times \cdots\]

Calculates final selling price after multiple successive discounts.

\(d_1, d_2\) = Discount percentages

Tips & Tricks

Tip: Use the formula \( SP = CP \times (1 \pm \text{Profit/Loss \%} / 100) \) directly to avoid separate profit or loss calculations.

When to use: When quick calculation of selling price is needed given profit or loss percentage.

Tip: For successive discounts, multiply the complements of each discount (i.e., \(1 - \frac{d}{100}\)) instead of adding discount percentages.

When to use: When dealing with multiple successive discounts to save time and avoid errors.

Tip: Remember that profit and loss percentages are always calculated on the cost price, not on the selling price.

When to use: To avoid confusion and mistakes in percentage calculations.

Tip: If profit % equals loss % on items with the same cost price, the overall result is always a loss.

When to use: For mixed profit and loss problems involving equal cost prices.

Tip: Convert all prices to INR and use metric units consistently to avoid unit mismatch.

When to use: In all numerical problems to maintain clarity and correctness.

Common Mistakes to Avoid

❌ Calculating profit or loss percentage on selling price instead of cost price.
✓ Always calculate profit or loss percentage using cost price as the base.
Why: Students confuse the base for percentage calculation, leading to incorrect answers.
❌ Adding discount percentages directly instead of applying them successively.
✓ Apply successive discounts one after another using multiplication of complements.
Why: Discounts are successive reductions, not additive.
❌ Mixing up profit and loss formulas or signs.
✓ Remember profit = SP - CP (positive if SP > CP), loss = CP - SP (positive if CP > SP).
Why: Sign confusion leads to wrong profit/loss determination.
❌ Ignoring units or currency in word problems.
✓ Always note and maintain units (INR, kg, meters) throughout calculations.
Why: Unit mismatch can cause conceptual errors and confusion.
❌ Forgetting to convert percentages into decimal form before calculations.
✓ Always divide percentage values by 100 when using them in formulas.
Why: Direct use of percentages without conversion leads to wrong numerical results.
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
Profit and Loss · 10 free messages
Ask me anything about this subtopic. You have 10 free messages this session — chat history isn't saved in preview.