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%)

**Marked Price and Discount:**

• Discount = MP − SP
• Discount% = (Discount / MP) × 100
• SP = MP × (100 − Discount%) / 100

**Successive Discounts:**

• For two discounts a% and b%: Effective discount = a + b − (a × b) / 100
• Net SP = MP × (100 − a) / 100 × (100 − b) / 100

**Markup and Profit Relationship:**

• If markup is M% on CP and discount is D% on MP:
• Net effect% = M − D − (M × D) / 100

**False Weight Formula:**

• Profit% = (True weight − False weight) / False weight × 100
• Or: Profit% = Error / (True value − Error) × 100

**Selling at Same Price:**

• If two articles are sold at the same SP, one at P% profit and one at P% loss:
• Net result = Always Loss = P² / 100 %

Worked Examples

**Example 1: Basic Profit Calculation** A shopkeeper buys an article for ₹800 and sells it for ₹920. Find the profit percentage.

*Solution:*

• Profit = 920 − 800 = ₹120
• Profit% = (120 / 800) × 100 = 15%

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**Example 2: MP, Discount, and Profit Combined** A trader marks his goods 40% above CP and offers a 20% discount. Find his profit percentage.

*Solution:*

• Let CP = 100
• MP = 100 + 40% of 100 = 140
• Discount = 20% of 140 = 28
• SP = 140 − 28 = 112
• Profit = 112 − 100 = 12
• Profit% = 12%

*Using formula:* Net% = 40 − 20 − (40 × 20) / 100 = 40 − 20 − 8 = 12%

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**Example 3: Successive Discounts** Find the single equivalent discount for successive discounts of 25% and 20%.

*Solution:*

• Effective discount = 25 + 20 − (25 × 20) / 100
• = 45 − 5 = 40%

*Verification:* Let MP = 100

• After 25%: 100 × 0.75 = 75
• After 20%: 75 × 0.80 = 60
• Total discount = 100 − 60 = 40%

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**Example 4: False Weight** A dishonest dealer claims to sell at CP but uses a weight of 900g instead of 1kg. Find his profit percentage.

*Solution:*

• Profit% = (1000 − 900) / 900 × 100
• = 100 / 900 × 100 = 11.11% or 100/9 %

Common Mistakes

• **Calculating profit% on SP instead of CP** → Always remember: Profit and Loss percentages are on Cost Price. Use CP as the base.

• **Adding successive discounts directly** → Two discounts of 15% and 10% ≠ 25%. Apply them sequentially or use the formula: 15 + 10 − (15 × 10)/100 = 23.5%.

• **Confusing discount base with profit base** → Discount% is on Marked Price; Profit% is on Cost Price. These are different amounts.

• **Assuming same SP with equal profit and loss means no net effect** → Selling two items at same SP with x% profit and x% loss always results in net loss of x²/100 %.

• **Ignoring "on cost" vs "on selling" in problem wording** → Read carefully whether percentage is stated "on cost price" or "on selling price"—this changes calculations entirely.

Quick Reference

• Profit% and Loss% → Always on CP
• Discount% → Always on MP
• Successive discounts a% and b% → Equivalent = a + b − ab/100
• Markup M%, Discount D% → Net = M − D − MD/100
• False weight gain% = (Error / Actual quantity given) × 100
• Same SP, P% profit and P% loss → Net Loss = P²/100 %