Profit, Loss and Discount — Study Notes

Overview

Profit, Loss and Discount is a cornerstone topic in SSC CGL Tier-1 Quantitative Aptitude, typically yielding 2–4 questions per exam. This chapter tests your ability to work with Cost Price (CP), Selling Price (SP), Marked Price (MP), profit percentages, loss percentages, and various discount schemes. The key is understanding the relationships between these values and converting word problems into simple equations.

Mastery here requires two skills: (1) instant recall of basic formulas, and (2) the ability to handle successive discounts and markup-discount combinations without confusion. Questions range from straightforward one-step calculations to multi-layered problems involving false weights, successive transactions, or combined profit-loss scenarios. Because the formulas are interconnected, a single conceptual error can cascade through an entire problem—so precision matters.

Strong performance on this topic directly boosts your overall Quantitative Aptitude score, as these questions are generally faster to solve than geometry or trigonometry once you have the formulas locked in.

Key Concepts

• **Cost Price (CP)** is the price at which an article is purchased or manufactured. **Selling Price (SP)** is the price at which it is sold. Profit occurs when SP > CP; loss occurs when SP < CP.

• **Profit % and Loss %** are always calculated on the Cost Price unless explicitly stated otherwise. Profit % = [(SP – CP)/CP] × 100; Loss % = [(CP – SP)/CP] × 100.

• **Marked Price (MP)** is the label price before any discount. **Discount** is a reduction on the MP. The relationship: SP = MP – Discount. Discount % is calculated on MP.

• **Successive Discounts** cannot be added directly. Two successive discounts of x% and y% combine to give a net discount of [x + y – (xy/100)]%. Alternatively, multiply the remaining fractions: SP = MP × (1 – x/100) × (1 – y/100).

• **Markup** is the amount or percentage added to CP to arrive at MP. If CP is increased by m% to get MP, then MP = CP × (1 + m/100). The final profit depends on both markup and discount.

• When an article is sold at a profit of p% and later at a loss of l%, the overall result depends on the individual transaction values. Each transaction's CP and SP must be tracked separately unless the same article is bought and sold repeatedly.

• **False weight** problems involve a shopkeeper using incorrect weights. If a trader uses a weight of w grams but claims it as W grams, effective CP per claimed unit is (w/W) × actual CP, and profit % must account for this difference.