Profit, Loss and Discount

Overview

Profit, Loss and Discount is a cornerstone arithmetic topic in IBPS PO Prelims, appearing consistently in both direct calculation questions and embedded within Data Interpretation sets. This topic tests your understanding of commercial transactions—how traders set prices, offer discounts, and calculate gains or losses.

Mastering this topic requires comfort with percentage calculations and the ability to quickly convert between Cost Price, Selling Price, and Marked Price. Questions range from straightforward single-step problems to multi-layered scenarios involving successive discounts, dishonest dealers, and false weights. Since IBPS PO Prelims demands speed (solving 35 questions in 20 minutes), memorizing shortcut formulas and recognizing problem patterns is essential for scoring well.

The good news: once you internalize the core relationships, most questions become mechanical. This topic connects directly with Percentage, Ratio, and Partnership problems, so strength here pays dividends across your quant preparation.

Key Concepts

• **Cost Price (CP)** is the amount paid to acquire goods. **Selling Price (SP)** is the amount received when selling. The difference determines profit or loss.

• **Profit occurs when SP > CP**; Loss occurs when SP < CP. Both are always calculated as a percentage of CP, not SP.

• **Marked Price (MP)** is the listed/sticker price before any discount. The relationship flows as: CP → MP (markup applied) → SP (discount applied).

• **Discount is always calculated on MP**, while profit/loss is calculated on CP. Confusing these bases is the most common error.

• **Successive discounts** are applied one after another on the reduced price, not on the original MP. Two discounts of 20% and 10% are NOT equal to 30%.

• **False weight problems** involve dealers who claim to sell at CP but cheat on quantity. The effective profit comes from the quantity shortfall.

• **Break-even** occurs when total revenue equals total cost (SP = CP), meaning zero profit and zero loss.

Formulas / Key Facts

**Basic Relationships:**

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

**Price Conversions:**

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