Profit and Loss
Overview
The questions at Clerk level are direct and formula-based — you'll rarely encounter complex scenarios involving successive discounts or dishonest dealings. Mastering this topic is essential because it shares concepts with Percentage, Ratio, and Simple Interest, creating a multiplier effect on your overall Quant score.
The core skill tested is your ability to quickly identify Cost Price (CP), Selling Price (SP), and Marked Price (MP) from word problems, then apply straightforward formulas. Speed matters more than complexity here — most Clerk-level questions can be solved in under 60 seconds if your fundamentals are solid.
Key Concepts
- Cost Price (CP) is what you pay to acquire an item; Selling Price (SP) is what you receive when selling it. Profit or Loss is always calculated on CP.
- Profit occurs when SP > CP; Loss occurs when SP < CP. The amount of profit or loss is simply the difference between SP and CP.
- Marked Price (MP) is the price tag on an item before any discount. The actual SP equals MP minus the discount given.
- Discount is always calculated on MP, while Profit/Loss percentage is always calculated on CP — mixing these bases is the most common error.
- Successive discounts are not additive. Two discounts of 10% and 20% do not equal 30%. They must be applied one after another on the reduced price.
- When CP and SP are given per unit, always ensure both refer to the same quantity before calculating profit/loss percentage.
- Break-even point means SP = CP, resulting in zero profit and zero loss.
Formulas / Key Facts
Basic Profit and Loss
- Profit = SP – CP
- Loss = CP – SP
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
Finding SP from Profit/Loss %
- SP = CP × (100 + Profit%) / 100
- SP = CP × (100 – Loss%) / 100
Finding CP from Profit/Loss %
- CP = SP × 100 / (100 + Profit%)
- CP = SP × 100 / (100 – Loss%)
Discount Formulas
- Discount = MP – SP
- Discount % = (Discount / MP) × 100
- SP = MP × (100 – Discount%) / 100
Successive Discounts
- For discounts of a% and b%: Effective SP = MP × (100 – a)/100 × (100 – b)/100
- Net single discount = a + b – (ab/100)
Relation between MP, CP, and Profit with Discount
- If profit is P% and discount is D%, then: MP/CP = (100 + P) / (100 – D)
Worked Examples
Example 1: Basic Profit Percentage A shopkeeper buys an article for ₹400 and sells it for ₹460. Find the profit percentage.
Solution:
- CP = ₹400, SP = ₹460
- Profit = 460 – 400 = ₹60
- Profit % = (60/400) × 100 = 15%
Answer: 15%
Example 2: Finding CP from Loss Percentage An item is sold for ₹1020 at a loss of 15%. What was the cost price?
Solution:
- SP = CP × (100 – Loss%) / 100
- 1020 = CP × 85/100
- CP = 1020 × 100/85 = ₹1200
Answer: ₹1200
Example 3: MP, Discount, and Profit Combined A trader marks an article 25% above the cost price and allows a discount of 10%. Find his profit percentage.
Solution:
- Let CP = ₹100
- MP = 100 + 25% of 100 = ₹125
- Discount = 10% of 125 = ₹12.50
- SP = 125 – 12.50 = ₹112.50
- Profit = 112.50 – 100 = ₹12.50
- Profit % = (12.50/100) × 100 = 12.5%
Alternative using formula:
- MP/CP = (100 + P)/(100 – D)
- 125/100 = (100 + P)/90
- 100 + P = 125 × 90/100 = 112.5
- P = 12.5%
Answer: 12.5%
Example 4: Successive Discounts The marked price of a shirt is ₹800. Two successive discounts of 10% and 15% are given. Find the selling price.
Solution:
- After first discount: 800 × 90/100 = ₹720
- After second discount: 720 × 85/100 = ₹612
Answer: ₹612
Common Mistakes
- Calculating profit % on SP instead of CP → Always remember: Profit/Loss percentage is based on Cost Price, never on Selling Price.
- Calculating discount on CP instead of MP → Discount percentage is always applied on Marked Price. The formula is Discount = (Discount/MP) × 100, not on CP.
- Adding successive discounts directly → Two discounts of 20% and 10% do not equal 30%. Apply them sequentially or use the formula: Net discount = 20 + 10 – (20×10)/100 = 28%.
- Confusing "% above CP" with "% profit" → If MP is 20% above CP, profit will be less than 20% if any discount is given. Read carefully whether the question mentions markup or actual profit.
- Ignoring units in bulk problems → If CP is given per dozen and SP per piece, convert to the same unit before calculating. Forgetting this leads to absurd profit percentages.
Quick Reference
- Profit % = (SP – CP)/CP × 100; Loss % = (CP – SP)/CP × 100
- SP = CP × (100 ± Profit or Loss %)/100
- Discount is on MP; Profit/Loss is on CP — never mix the bases
- Successive discounts a% and b%: Net = a + b – ab/100
- To gain P% after giving D% discount: MP = CP × (100+P)/(100–D)
- No profit no loss means SP = CP