FORMULA CHAPTER

Chapter 10 – Profit and Loss

WBBSEClass 09Mathematics8 formulas

Complete WBBSE Madhyamik Class 9 Profit and Loss formula list with cost price, selling price, percentages and worked examples for exam preparation.

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Profit = SP − CP

$\text{Profit Percentage}=\frac{\text{Profit}}{\text{CP}}\times100$

$SP=\frac{100+\text{Profit }\%}{100}\times CP$

$CP=\frac{100}{100+\text{Profit }\%}\times SP$

Loss = CP − SP

$\text{Loss Percentage}=\frac{\text{Loss}}{\text{CP}}\times100$

$SP=\frac{100-\text{Loss }\%}{100}\times CP$

$CP=\frac{100}{100-\text{Loss }\%}\times SP$

Profit

Profit = SP − CP

SymbolMeaningUnit

CPCost Pricecurrency units

SPSelling Pricecurrency units

ProfitAmount gainedcurrency units

Worked example

Question: An article is bought for ₹800 and sold for ₹950. Find the profit.

Calculation:

Step 1: CP = ₹800 and SP = ₹950.

Step 2: Profit = SP − CP.

Step 3: Profit = 950 − 800 = ₹150.

Answer: The profit is ₹150.

Profit Percentage

$\text{Profit Percentage}=\frac{\text{Profit}}{\text{CP}}\times100$

SymbolMeaningUnit

ProfitSelling price minus cost pricecurrency units

CPCost Pricecurrency units

Profit %Profit percentagepercent

Worked example

Question: A shopkeeper earns ₹120 profit on an article costing ₹600. Find the profit percentage.

Calculation:

Step 1: Profit = ₹120 and CP = ₹600.

Step 2: Profit % = (Profit ÷ CP) × 100.

Step 3: Profit % = (120 ÷ 600) × 100 = 20%.

Answer: The profit percentage is 20%.

Selling Price at a Profit

$SP=\frac{100+\text{Profit }\%}{100}\times CP$

SymbolMeaningUnit

CPCost Pricecurrency units

SPSelling Pricecurrency units

Profit %Profit percentagepercent

Worked example

Question: Find the selling price of an article costing ₹500 at a profit of 20%.

Calculation:

Step 1: CP = ₹500 and Profit % = 20%.

Step 2: SP = [(100 + 20) ÷ 100] × 500.

Step 3: SP = 1.2 × 500 = ₹600.

Answer: The selling price is ₹600.

Cost Price from Profit Percentage

$CP=\frac{100}{100+\text{Profit }\%}\times SP$

SymbolMeaningUnit

CPCost Pricecurrency units

SPSelling Pricecurrency units

Profit %Profit percentagepercent

Worked example

Question: An article is sold for ₹720 at a profit of 20%. Find its cost price.

Calculation:

Step 1: SP = ₹720 and Profit % = 20%.

Step 2: CP = [100 ÷ (100 + 20)] × 720.

Step 3: CP = (100 ÷ 120) × 720 = ₹600.

Answer: The cost price is ₹600.

Loss

Loss = CP − SP

SymbolMeaningUnit

CPCost Pricecurrency units

SPSelling Pricecurrency units

LossAmount lostcurrency units

Worked example

Question: An article costing ₹900 is sold for ₹810. Find the loss.

Calculation:

Step 1: CP = ₹900 and SP = ₹810.

Step 2: Loss = CP − SP.

Step 3: Loss = 900 − 810 = ₹90.

Answer: The loss is ₹90.

Loss Percentage

$\text{Loss Percentage}=\frac{\text{Loss}}{\text{CP}}\times100$

SymbolMeaningUnit

LossCost price minus selling pricecurrency units

CPCost Pricecurrency units

Loss %Loss percentagepercent

Worked example

Question: A trader loses ₹75 on an article costing ₹500. Find the loss percentage.

Calculation:

Step 1: Loss = ₹75 and CP = ₹500.

Step 2: Loss % = (Loss ÷ CP) × 100.

Step 3: Loss % = (75 ÷ 500) × 100 = 15%.

Answer: The loss percentage is 15%.

Selling Price at a Loss

$SP=\frac{100-\text{Loss }\%}{100}\times CP$

SymbolMeaningUnit

CPCost Pricecurrency units

SPSelling Pricecurrency units

Loss %Loss percentagepercent

Worked example

Question: Find the selling price of an article costing ₹800 at a loss of 10%.

Calculation:

Step 1: CP = ₹800 and Loss % = 10%.

Step 2: SP = [(100 − 10) ÷ 100] × 800.

Step 3: SP = 0.9 × 800 = ₹720.

Answer: The selling price is ₹720.

Cost Price from Loss Percentage

$CP=\frac{100}{100-\text{Loss }\%}\times SP$

SymbolMeaningUnit

SPSelling Pricecurrency units

Loss %Loss percentagepercent

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