Profit and Loss — Study Notes for UP Police Constable

Overview

Profit and Loss is a high-frequency topic in the Numerical & Mental Ability section of UP Police Constable exams, typically yielding 3–5 questions. This topic tests your ability to calculate commercial transactions, understand pricing strategies, and solve real-world buying-selling scenarios under time pressure.

The core challenge is distinguishing between Cost Price (CP), Selling Price (SP), and Marked Price (MP), then applying formulas accurately. Questions often involve successive discounts, false weights, and combination scenarios that require multi-step calculations. Mastering this topic requires memorizing key formulas and practicing quick mental calculations, as the exam rewards speed alongside accuracy.

Understanding percentage conversions is crucial — most profit/loss problems boil down to percentage increase or decrease calculations. Students who can instantly recall formulas and avoid sign errors (profit vs loss) typically score full marks in this section.

Key Concepts

• **Cost Price (CP)** is the amount paid to acquire or produce an item. All profit/loss calculations reference this baseline.

• **Selling Price (SP)** is the amount received when selling the item. Profit occurs when SP > CP; loss occurs when SP < CP.

• **Marked Price (MP)** is the listed or tagged price before any discount. Discount is always calculated on MP, not CP.

• **Profit** is calculated as SP − CP, while **Loss** is CP − SP. Profit% and Loss% are always calculated on CP unless stated otherwise.

• **Discount** reduces the MP to arrive at the final SP. A single discount differs from successive discounts — two 10% discounts do NOT equal 20%.

• **Break-even** occurs when SP = CP, meaning neither profit nor loss. This concept appears in problems involving partial sales.

• **False weight/measure** creates an implicit profit by giving less quantity while charging for more — a common trick question type.

• In **partnership/mix problems**, profit distribution follows the ratio of investments or quantities, connecting profit-loss with ratio concepts.

Formulas / Key Facts

**Basic Formulas:**

• Profit = SP − CP
• Loss = CP − SP
• Profit% = (Profit / CP) × 100 = [(SP − CP) / CP] × 100
• Loss% = (Loss / CP) × 100 = [(CP − SP) / CP] × 100
• SP = CP × (100 + Profit%) / 100 = CP × (100 − Loss%) / 100
• CP = SP × 100 / (100 + Profit%) = SP × 100 / (100 − Loss%)