Profit, Loss & Discount

🎯 1. Learning Objectives

Identify cost price, selling price and marked price.
Calculate profit, loss and their percentages.
Find selling or cost price from a percentage.
Calculate discount and successive discounts.
Combine markup and discount correctly.
Solve reverse-price and placement-style business problems.

📖 2. Basic Terms

Cost Price (CP)

The amount paid to obtain or produce an item.

Selling Price (SP)

The amount received when the item is sold.

Profit

Profit = SP − CP

Loss

Loss = CP − SP

📌 3. Profit and Loss Percentages

Profit Percentage

Profit% = Profit/CP × 100

Loss Percentage

Loss% = Loss/CP × 100

The denominator is CP: profit and loss percentages are normally calculated on cost price unless the question explicitly says otherwise.

🔄 4. Finding SP or CP

SP at p% Profit

SP = CP(1+p/100)

SP at p% Loss

SP = CP(1−p/100)

CP from Profit SP

CP = SP/(1+p/100)

CP from Loss SP

CP = SP/(1−p/100)

🏷️ 5. Marked Price and Discount

Marked price (MP) is the displayed price before a discount.

Discount

Discount = MP − SP

Discount Percentage

Discount% = Discount/MP × 100

Price after Discount

SP = MP(1−d/100)

Recover Marked Price

MP = SP/(1−d/100)

🔁 6. Successive Discounts

Discounts are applied one after another, not added directly.

Equivalent discount = d₁+d₂−d₁d₂/100

Example: 20% followed by 10% gives 20+10−2=28%, not 30%.

📈 7. Markup Followed by Discount

Apply both multipliers to the cost price.

Final SP = CP(1+markup/100)(1−discount/100)

Example: 25% markup followed by 20% discount gives 1.25×0.80=1, so SP=CP.

↩️ 8. Reverse and Special Relations

Profit as % of SP

If profit is p% of SP, convert using CP=SP−profit before finding profit% on CP.

Same SP, Equal Profit and Loss %

Net loss% = p²/100

One item at p% profit and another at p% loss, both at the same SP.

INTERACTIVE EXPLORER

🧪 9. Pricing Explorer

Select a calculation, enter values and click Calculate. Input changes hide the old result.

Calculation

Cost price

Selling price

Not required

Select a calculation or example, then click Calculate.

🧾 10. Solved Examples

Example 1: Profit

Problem: CP ₹500, SP ₹600.

Solution: Profit ₹100; profit%=100/500×100=20%.

Example 2: Loss

Problem: CP ₹800, SP ₹720.

Solution: Loss ₹80; loss%=80/800×100=10%.

Example 3: Discount

Problem: MP ₹1,000 with 20% discount.

Solution: SP=1000×0.80=₹800.

Example 4: Reverse CP

Problem: SP ₹690 at 15% profit.

Solution: CP=690/1.15=₹600.

💻 11. Pricing in Programming

E-commerce

Shopping applications calculate discounts, offers and final cart prices.

Inventory

Systems compare acquisition cost, selling price and product margin.

Dynamic Pricing

Programs adjust markup and discounts using demand and stock.

Business Analytics

Dashboards report gross margin, loss rates and promotion performance.

⚠️ 12. Common Mistakes

Wrong Base

Profit/loss percentage uses CP; discount percentage uses MP.

Adding Successive Discounts

Multiply remaining-price factors instead.

Confusing MP and CP

Marked price is a display price; cost price is the seller’s cost.

Reversing with Subtraction

Recover original prices by division, not by simply adding the percentage.

✍️ 13. Practice Problems

Solve first, then use Show Solution.

1. CP ₹400, SP ₹460. Find profit%.

2. CP ₹900, loss 20%. Find SP.

3. MP ₹2,000, discount 15%. Find SP.

4. Discounts 10% and 20%. Find equivalent discount.

5. SP ₹960 at 20% profit. Find CP.

📝 14. Quick Revision

Profit=SP−CP; loss=CP−SP.
Profit% and loss% normally use CP.
Discount=MP−SP; discount% uses MP.
At p% profit, SP=CP(1+p/100).
At p% loss, SP=CP(1−p/100).
After d% discount, SP=MP(1−d/100).
Two discounts d₁,d₂ combine to d₁+d₂−d₁d₂/100.
Reverse calculations divide by the relevant multiplier.

INTERACTIVE PRACTICE