ARITHMETIC: PROFIT & LOSS
Comprehensive Concepts, Formulas, Worked Examples & 20 Practice MCQs
Arithmetic is a foundational branch of mathematics that deals with numbers and numerical operations. Within business and
everyday commerce, Profit and Loss is one of the most critical practical topics, used to analyze financial transactions and
calculate performance, margins, and yield.
1. CORE CONCEPTS & DEFINITIONS
Cost Price (CP): The total price at which an article is acquired by the seller. It encompasses the base purchase price
along with all additional overhead expenses such as freight, labor, taxes, or reconditioning.
Effective CP = Purchase Price + Overhead Expenses
Selling Price (SP): The price at which an article is transferred or sold to the buyer.
Profit (Gain): Realized when the Selling Price exceeds the Cost Price (SP > CP).
Profit = SP − CP
Loss: Incurred when the Cost Price exceeds the Selling Price (CP > SP).
Loss = CP − SP
Marked Price (MP) & Discount: Marked Price (or List Price) is the price quoted or labeled on an item. A discount is a
deduction given on the Marked Price.
Discount = MP − SP
2. FUNDAMENTAL FORMULAS
Note: Unless explicitly stated otherwise, profit and loss percentages are always calculated relative to the Cost Price (CP).
1. Profit & Loss Percentages:
• Profit % = (Profit / CP) × 100
• Loss % = (Loss / CP) × 100
2. Calculating Selling Price (SP):
• When Profit: SP = CP × [(100 + Profit %) / 100]
• When Loss: SP = CP × [(100 − Loss %) / 100]
3. Calculating Cost Price (CP):
• When Profit: CP = SP × [100 / (100 + Profit %)]
• When Loss: CP = SP × [100 / (100 − Loss %)]
Arithmetic — Profit and Loss Study Guide Page 1 of 4
Comprehensive Concepts, Formulas, Worked Examples & 20 Practice MCQs
Arithmetic is a foundational branch of mathematics that deals with numbers and numerical operations. Within business and
everyday commerce, Profit and Loss is one of the most critical practical topics, used to analyze financial transactions and
calculate performance, margins, and yield.
1. CORE CONCEPTS & DEFINITIONS
Cost Price (CP): The total price at which an article is acquired by the seller. It encompasses the base purchase price
along with all additional overhead expenses such as freight, labor, taxes, or reconditioning.
Effective CP = Purchase Price + Overhead Expenses
Selling Price (SP): The price at which an article is transferred or sold to the buyer.
Profit (Gain): Realized when the Selling Price exceeds the Cost Price (SP > CP).
Profit = SP − CP
Loss: Incurred when the Cost Price exceeds the Selling Price (CP > SP).
Loss = CP − SP
Marked Price (MP) & Discount: Marked Price (or List Price) is the price quoted or labeled on an item. A discount is a
deduction given on the Marked Price.
Discount = MP − SP
2. FUNDAMENTAL FORMULAS
Note: Unless explicitly stated otherwise, profit and loss percentages are always calculated relative to the Cost Price (CP).
1. Profit & Loss Percentages:
• Profit % = (Profit / CP) × 100
• Loss % = (Loss / CP) × 100
2. Calculating Selling Price (SP):
• When Profit: SP = CP × [(100 + Profit %) / 100]
• When Loss: SP = CP × [(100 − Loss %) / 100]
3. Calculating Cost Price (CP):
• When Profit: CP = SP × [100 / (100 + Profit %)]
• When Loss: CP = SP × [100 / (100 − Loss %)]
Arithmetic — Profit and Loss Study Guide Page 1 of 4
