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.

• **Dishonest dealer tricks**: claiming to sell at CP but using false weights, or mixing profit% with discount% on different bases—always identify the reference base (CP or MP) before calculating.

Formulas / Key Facts

1. **Profit = SP – CP**; **Loss = CP – SP** 2. **Profit % = [(SP – CP)/CP] × 100 = [(Profit)/CP] × 100** 3. **Loss % = [(CP – SP)/CP] × 100 = [(Loss)/CP] × 100** 4. **SP = CP × (1 + Profit%/100)** when profit is given 5. **SP = CP × (1 – Loss%/100)** when loss is given 6. **CP = SP / (1 + Profit%/100)** or **CP = SP / (1 – Loss%/100)** depending on profit or loss 7. **Discount = MP – SP**; **Discount % = [(MP – SP)/MP] × 100** 8. **SP = MP × (1 – Discount%/100)** 9. **Successive Discounts**: Net discount % = x + y – (xy/100) for two discounts of x% and y% 10. **Markup relation**: MP = CP × (1 + Markup%/100). Then apply discount on MP to get SP. 11. **Overall profit/loss after two transactions**: If first transaction gives x% profit and second gives y% loss, overall % = [x – y – (xy/100)]. Sign indicates profit (+) or loss (–). 12. **Break-even**: SP = CP (no profit, no loss). Profit% = 0%.

Worked Examples

**Example 1: Basic Profit %** A shopkeeper buys an article for ₹500 and sells it for ₹650. Find the profit %.

*Solution:* CP = 500, SP = 650 Profit = SP – CP = 650 – 500 = 150 Profit % = (150/500) × 100 = 30%

**Example 2: Successive Discounts** An article is marked at ₹2000. Two successive discounts of 20% and 10% are given. Find the final selling price.

*Solution:* Method 1 (formula): Net discount % = 20 + 10 – (20×10/100) = 30 – 2 = 28% SP = 2000 × (1 – 28/100) = 2000 × 0.72 = ₹1440

Method 2 (step-by-step): After 20% discount: 2000 × 0.8 = 1600 After 10% discount on 1600: 1600 × 0.9 = ₹1440

**Example 3: Markup and Discount Combined** A trader marks an article 40% above its cost price and then allows a discount of 20%. Find his profit %.

*Solution:* Let CP = 100 MP = 100 × 1.4 = 140 Discount = 20% of MP = 0.2 × 140 = 28 SP = 140 – 28 = 112 Profit = 112 – 100 = 12 Profit % = (12/100) × 100 = 12%

Alternatively (formula approach): Profit % = m – d – (md/100) where m = markup%, d = discount% = 40 – 20 – (40×20/100) = 20 – 8 = 12%

**Example 4: Finding CP when SP and Profit % are Given** An article is sold for ₹960 at a profit of 20%. What was the cost price?

*Solution:* SP = CP × (1 + 20/100) = CP × 1.2 960 = CP × 1.2 CP = 960 / 1.2 = ₹800

Common Mistakes

• **Adding successive discounts directly**: Students often add 20% + 10% = 30% for successive discounts. Correct fix: Use the formula x + y – (xy/100) or multiply the remaining fractions step-by-step.

• **Confusing the base for profit/loss %**: Calculating profit % on SP instead of CP, or discount % on SP instead of MP. Correct fix: Always remember profit% and loss% use CP as base; discount% uses MP as base.

• **Markup-discount confusion**: Applying discount % directly to CP instead of first calculating MP. Correct fix: First find MP = CP × (1 + markup%/100), then apply discount on MP to get SP.

• **Sign errors in overall profit/loss**: Forgetting that loss is negative when using combined profit/loss formula. Correct fix: Use the formula [x – y – (xy/100)] carefully, where x is profit% (positive) and y is loss% (positive value but represents loss).

• **Misinterpreting "sold at CP but used false weight"**: Assuming no profit because price equals CP. Correct fix: False weight means effective CP is lower, so there is hidden profit even when claiming to sell at CP. Calculate effective CP using the weight ratio.

Quick Reference

• Profit % = [(SP – CP)/CP] × 100; always on CP base
• Loss % = [(CP – SP)/CP] × 100; always on CP base
• Discount % = [(MP – SP)/MP] × 100; always on MP base
• Successive discounts of x% and y%: Net = x + y – (xy/100)
• Markup m%, Discount d%: Profit % = m – d – (md/100)
• SP = CP for break-even (zero profit, zero loss)