Profit and Loss
Overview
Profit and Loss is one of the most frequently tested topics in MPESB Group 1/2/3 mathematics. It forms the foundation for understanding commercial arithmetic and directly connects to everyday transactions. Questions typically range from basic profit/loss percentage calculations to complex problems involving marked price, successive discounts, and dishonest dealings.
This topic carries significant weightage because it tests both conceptual understanding and calculation speed. Students who master the underlying relationships between Cost Price, Selling Price, Marked Price, and Discount can solve most problems within 30-60 seconds. The key is understanding that all these quantities are interconnected through simple percentage relationships.
Problems may involve real-world scenarios like shopkeeper transactions, manufacturing costs, or trade discounts.
Key Concepts
- Cost Price (CP) is the price at which an article is purchased or manufactured; it includes all expenses incurred to bring the goods to a saleable condition.
- Selling Price (SP) is the price at which an article is sold to the customer; profit occurs when SP > CP, loss occurs when SP < CP.
- Marked Price (MP) is the price tagged or listed on the article before any discount; it is always calculated on CP, and discount is always calculated on MP.
- Discount is the reduction given on Marked Price to arrive at Selling Price; successive discounts are applied one after another on reduced prices, not on original MP.
- Profit or Loss percentage is always calculated on Cost Price unless explicitly stated otherwise.
- In dishonest dealing problems, a trader uses faulty weights or measures; the profit percentage depends on the ratio of actual quantity to claimed quantity.
- Break-even point occurs when SP equals CP, resulting in neither profit nor loss.
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%)
Marked Price and Discount:
- Discount = MP − SP
- Discount% = (Discount / MP) × 100
- SP = MP × (100 − Discount%) / 100
- If Profit% = P and Discount% = D, then MP = CP × (100 + P) / (100 − D)
Successive Discounts:
- For two discounts of a% and b%, equivalent single discount = (a + b − ab/100)%
Dishonest Dealer:
- Profit% = [(True Weight − False Weight) / False Weight] × 100
- Or simply: Profit% = (Error / Claimed Quantity) × 100
Useful Shortcut:
- If CP of x articles = SP of y articles, then Profit% = [(x − y) / y] × 100 (profit if x > y, loss if x < y)
Worked Examples
Example 1: Basic Profit Calculation 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: Marked Price with Discount A trader marks his goods 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%
Answer: 12.5%
Example 3: Successive Discounts Two successive discounts of 20% and 10% are given on an article with marked price ₹500. Find the selling price.
Solution:
- After first discount: SP₁ = 500 × (100 − 20)/100 = 500 × 0.80 = ₹400
- After second discount: SP₂ = 400 × (100 − 10)/100 = 400 × 0.90 = ₹360
Alternative using formula:
- Equivalent discount = 20 + 10 − (20 × 10)/100 = 30 − 2 = 28%
- SP = 500 × (100 − 28)/100 = 500 × 0.72 = ₹360
Answer: ₹360
Example 4: Dishonest Dealer A shopkeeper claims to sell at cost price but uses a weight of 900 grams instead of 1 kg. Find his profit percentage.
Solution:
- He gives 900 gm but charges for 1000 gm
- Profit% = [(1000 − 900) / 900] × 100 = (100/900) × 100 = 11.11%
Answer: 11.11% or 11⅑%
Example 5: CP of x equals SP of y The cost price of 15 articles is equal to the selling price of 12 articles. Find the profit or loss percentage.
Solution:
- CP of 15 = SP of 12
- Let CP of 1 article = ₹1, so CP of 15 = ₹15
- SP of 12 articles = ₹15, so SP of 1 article = 15/12 = ₹1.25
- Profit per article = 1.25 − 1 = ₹0.25
- Profit% = (0.25/1) × 100 = 25%
Answer: 25% profit
Common Mistakes
- Calculating percentage on SP instead of CP: Profit% and Loss% are always computed on Cost Price. Students often divide profit by SP, leading to wrong answers.
- Adding successive discounts directly: Two discounts of 20% and 10% do NOT equal 30%. Apply them sequentially or use the equivalent discount formula.
- Confusing Marked Price with Selling Price: MP is the listed price; SP is what the customer actually pays after discount. Discount is always on MP, profit is always on CP.
- Ignoring expenses in Cost Price: When a problem mentions transportation, repair, or overhead costs, add them to purchase price to get true CP.
- Reversing the dishonest dealer formula: The denominator should be the false/claimed quantity (what the dealer claims to give), not the true quantity.
Quick Reference
- Profit% = (SP − CP)/CP × 100; always on CP
- MP is for discount calculation; CP is for profit calculation
- Successive discounts a% and b% = (a + b − ab/100)%
- Dishonest dealer profit% = (Error/False measure) × 100
- CP of m = SP of n → Profit% = (m−n)/n × 100
- No profit no loss means SP = CP