Profit and Loss

Profit and Loss are essential concepts in arithmetic used to evaluate financial transactions involving the buying and selling of goods or services. These concepts are widely used in business, economics, trade, and even daily life decisions like shopping.

Understanding how to calculate profit or loss helps in making better financial choices, estimating costs, and analyzing gains or losses in any deal.

---

🔹 Key Terms and Definitions

1. Cost Price (CP):
   The amount paid to purchase an article.
   📌 Example: If a pen is bought for ₹20, then CP = ₹20

2. Selling Price (SP):
   The amount received by selling the article.
   📌 Example: If the pen is sold for ₹25, then SP = ₹25

3. Profit (or Gain):
   When SP > CP, the seller earns a profit.
   📌 Formula: Profit = SP - CP
   📌 Example: CP = ₹100, SP = ₹120 → Profit = ₹20

4. Loss:
   When CP > SP, the seller incurs a loss.
   📌 Formula: Loss = CP - SP
   📌 Example: CP = ₹200, SP = ₹180 → Loss = ₹20

---

🔹 Percentage Calculations

Percentage values give us a clearer idea of how significant the profit or loss is compared to the cost.

1. Percentage Profit:

   $$\text{Percentage Profit}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$$

2. Percentage Loss:

   $$\text{Percentage Loss}=\left(\frac{\text{Loss}}{\text{CP}}\right)\times 100$$

📌 Example:
CP = ₹500, SP = ₹600 → Profit = ₹100
Percentage Profit = (100 / 500) × 100 = 20%

---

🔹 Marked Price, Discount, and Profit

In retail:

• Marked Price (MP): Printed price before any discount.

• Discount: A reduction offered on the marked price.

• Selling Price (SP): Final price after applying the discount.

• Profit or Loss is then calculated based on the actual Cost Price (CP).

📌 Example:
CP = ₹400
Marked Price = ₹500
Discount = 10% → SP = ₹500 - 10% of ₹500 = ₹450
Profit = SP - CP = ₹450 - ₹400 = ₹50 → Profit % = (50/400) × 100 = 12.5%

---

🔹 Successive Profit and Loss

If an article is sold multiple times with different profit or loss percentages:

Use the formula:

$$\text{Net \% change}=x+y+\frac{xy}{\mathrm{100}}$$

(where x and y are gains/losses. Use a negative sign for loss.)

📌 Example:
First sale: +20%, second sale: -10%
Net % = 20 - 10 + (20×(-10)/100) = 10 - 2 = 8% profit

---

🔹 Summary of Key Formulas

Concept	Formula
Profit	SP - CP
Loss	CP - SP
Percentage Profit	(Profit / CP) × 100
Percentage Loss	(Loss / CP) × 100
SP (when profit)	CP + Profit
SP (when loss)	CP - Loss
CP (when profit)	SP / (1 + Profit%) × 100
CP (when loss)	SP / (1 - Loss%) × 100
Net % Change (x & y)	x + y + (xy / 100)

---

📝 Practice Questions (MCQs)

1. A trader buys an article for ₹1,200 and sells it for ₹1,500. What is the profit percentage?

A) 20%
B) 25%
C) 30%
D) 40%

✅ Answer: B) 25%
Explanation:
Profit = 1500 - 1200 = ₹300
Percentage Profit = (300 / 1200) × 100 = 25%

2. A man bought a mobile phone for ₹6,000 and sold it at a 10% loss. What is the Selling Price?

A) ₹5,400
B) ₹5,600
C) ₹5,800
D) ₹6,100

✅ Answer: A) ₹5,400
Explanation:
Loss = 10% of 6000 = ₹600
SP = CP - Loss = 6000 - 600 = ₹5400

3. An item is marked at ₹800. A shopkeeper offers a 15% discount and still makes a 10% profit. What is the Cost Price?

A) ₹600
B) ₹620
C) ₹680
D) ₹700

✅ Answer: A) ₹600
Explanation:
Selling Price after discount = ₹800 - 15% = ₹680
Profit = 10% → SP = 110% of CP → 1.1 × CP = 680
CP = 680 / 1.1 = ₹600

4. A person sells two items at ₹500 each. On one, he gains 25%, and on the other, he loses 25%. What is the overall result?

A) No profit, no loss
B) 6.25% profit
C) 6.25% loss
D) 12.5% loss

✅ Answer: C) 6.25% loss
Explanation:
When gain and loss % are equal on the same SP, there is always a loss.
Net Loss % = (25 × 25)/100 = 6.25%

5. A shopkeeper earns a profit of 20% after giving a discount of 10% on the Marked Price. If the Selling Price is ₹540, what is the Cost Price?

A) ₹400
B) ₹420
C) ₹450
D) ₹500

✅ Answer: B) ₹450
Explanation:
Profit = 20% → SP = 1.2 × CP
540 = 1.2 × CP → CP = 540 / 1.2 = ₹450