Profit and Loss
Overview
Profit and Loss is a cornerstone topic in SBI Clerk Prelims Numerical Ability, appearing both as standalone questions and embedded within Data Interpretation sets. The topic tests your ability to quickly calculate buying prices, selling prices, discounts, and profit percentages—skills that mirror real-world commerce scenarios.
The questions are typically straightforward but designed to trap students who confuse the base for percentage calculations. Mastering this topic requires absolute clarity on which value serves as the base (Cost Price for profit/loss, Marked Price for discount) and the ability to perform quick mental calculations with common percentage-fraction equivalents.
Key Concepts
- Cost Price (CP): The price at which an article is purchased or manufactured. This is always the base for calculating profit or loss percentage.
- Selling Price (SP): The price at which an article is sold to a customer. SP > CP means profit; SP < CP means loss.
- Marked Price (MP): The price displayed on the product tag before any discount. Also called List Price or Catalogue Price.
- Discount: Reduction offered on the Marked Price. Discount is always calculated on MP, never on CP.
- Profit/Loss Percentage: Always calculated on Cost Price unless explicitly stated otherwise.
- Successive Discounts: When multiple discounts are applied one after another, each discount applies to the reduced price from the previous discount, not the original MP.
- False Weight Concept: When a trader uses faulty weights, the profit percentage equals (Error/True Weight) × 100.
Formulas / Key Facts
Basic Formulas:
- Profit = SP − CP
- Loss = CP − SP
- Profit% = (Profit/CP) × 100
- Loss% = (Loss/CP) × 100
- SP = CP × (100 + Profit%)/100
- SP = CP × (100 − Loss%)/100
- CP = SP × 100/(100 + Profit%)
- CP = SP × 100/(100 − Loss%)
Discount Formulas:
- Discount = MP − SP
- Discount% = (Discount/MP) × 100
- SP = MP × (100 − Discount%)/100
Quick Multipliers:
- 10% profit → SP = 1.1 × CP
- 20% profit → SP = 1.2 × CP
- 25% profit → SP = 1.25 × CP
- 10% loss → SP = 0.9 × CP
- 20% discount → SP = 0.8 × MP
Successive Discounts:
- Two successive discounts of a% and b% give effective discount = a + b − (ab/100)%
Break-even and Special Cases:
- If CP and SP are equal, there is no profit or loss
- When goods worth Rs. X are sold at the CP of goods worth Rs. Y: Profit% = [(Y−X)/X] × 100
Worked Examples
Example 1: Basic Profit Calculation A shopkeeper buys an article for Rs. 400 and sells it at 15% profit. Find the selling price.
Solution: SP = CP × (100 + Profit%)/100 SP = 400 × (115/100) SP = 400 × 1.15 = Rs. 460
Example 2: Finding CP from SP and Profit% An article is sold for Rs. 720 at a profit of 20%. What is the cost price?
Solution: CP = SP × 100/(100 + Profit%) CP = 720 × 100/120 CP = 720 × 5/6 = Rs. 600
Example 3: MP, Discount, and Profit Combined A trader marks his goods 40% above cost price and allows a discount of 20%. 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% = (12/100) × 100 = 12%
Shortcut Formula: When marked up by m% and discount of d%, Profit% = m − d − (md/100) = 40 − 20 − (40×20/100) = 40 − 20 − 8 = 12%
Example 4: Successive Discounts Find the single equivalent discount for successive discounts of 20% and 10%.
Solution: Effective discount = 20 + 10 − (20×10/100) = 30 − 2 = 28%
Common Mistakes
- Wrong base for percentage calculation → Profit/Loss% is always on CP; Discount% is always on MP. A 20% markup followed by 20% discount does NOT give break-even—it gives a 4% loss.
- Adding successive discounts directly → Two discounts of 10% and 20% do not equal 30%. Apply them successively: effective discount is 28%.
- Confusing "profit on SP" problems → When a question says "profit is 25% of SP" (not CP), use the relation: Profit% on CP = (25/75) × 100 = 33.33%.
- Ignoring the word "each" → If 5 articles are bought for Rs. 100 and 4 are sold for Rs. 100, calculate per-article CP and SP before finding profit%.
- Misreading "sold at loss of" vs "sold at" → "Sold at 20% loss" means SP = 80% of CP. "Sold at loss of Rs. 20" means SP = CP − 20.
Quick Reference
- Profit% = (SP − CP)/CP × 100 — base is always CP
- Discount% = (MP − SP)/MP × 100 — base is always MP
- 25% profit means SP = 1.25 × CP (multiplier = 1.25)
- Successive discounts a%, b%: Net = a + b − ab/100
- Markup m%, Discount d%: Profit% = m − d − md/100
- False weight gain: Profit% = (Error/True Value) × 100