Profit & Loss
Overview
Profit & Loss is one of the most scoring topics in the Mathematics section of Maharashtra Police Bharti exam. Questions typically involve calculating profit percentage, loss percentage, selling price, or finding the cost price when other values are given. You will also encounter problems combining marked price, discount, and successive discounts.
This topic directly connects to your daily life — buying and selling goods — making it intuitive once you master the basic relationships. Most questions are straightforward formula applications, but examiners create complexity through discount chains, dishonest dealer problems, or mixing profit on one item with loss on another.
Mastering CP-SP-MP relationships and percentage calculations here will also help you in Percentage and Ratio-Proportion questions, as the underlying arithmetic is identical.
Key Concepts
- Cost Price (CP) is the price at which a trader buys goods. This is your base for calculating profit or loss.
- Selling Price (SP) is the price at which goods are sold to the customer. SP > CP means profit; SP < CP means loss.
- Marked Price (MP) is the price written on the product label (also called list price or tag price). Discount is always calculated on MP, not on CP.
- Profit or Loss is always calculated on CP — this is the universal rule unless the question explicitly states otherwise.
- Discount is always calculated on MP — the reduction given from the labelled price before arriving at SP.
- Successive discounts are applied one after another on the reduced price, not on the original MP.
- Break-even point occurs when SP = CP, meaning neither profit nor loss.
- In dishonest dealer problems, profit comes from using faulty weights/measures while claiming to sell at CP or at a stated profit percentage.
Formulas / Key Facts
Basic Relationships:
- Profit = SP − CP
- Loss = CP − SP
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
Finding SP from CP:
- When profit: SP = CP × (100 + Profit%) / 100
- When loss: SP = CP × (100 − Loss%) / 100
Finding CP from SP:
- When profit: CP = SP × 100 / (100 + Profit%)
- When loss: CP = SP × 100 / (100 − Loss%)
Marked Price and Discount:
- Discount = MP − SP
- Discount % = (Discount / MP) × 100
- SP = MP × (100 − Discount%) / 100
Successive Discounts (d₁% and d₂%):
- Effective SP = MP × (100 − d₁)/100 × (100 − d₂)/100
- Single equivalent discount for two successive discounts: d₁ + d₂ − (d₁ × d₂)/100
Dishonest Dealer (uses false weight):
- Profit % = [(True weight − False weight) / False weight] × 100
- If he also charges profit: Gain % = [(100 + Profit%) × (True weight / False weight)] − 100
Same article sold at profit and loss (equal percentage):
- When CP is same and one sells at x% profit and another at x% loss, there is always a net loss.
- Net Loss % = x²/100
Worked Examples
Example 1: Basic Profit Calculation
A shopkeeper buys a chair for ₹800 and sells it for ₹920. Find the profit percentage.
Solution:
- Profit = SP − CP = 920 − 800 = ₹120
- Profit % = (120 / 800) × 100 = 15%
Answer: 15% profit
Example 2: Finding CP when SP and Loss% given
A mobile phone is sold for ₹8,550 at a loss of 5%. What was the cost price?
Solution:
- SP = CP × (100 − Loss%) / 100
- 8550 = CP × 95/100
- CP = 8550 × 100/95 = ₹9,000
Answer: ₹9,000
Example 3: Marked Price with Discount
A shirt is marked at ₹1,200. The shopkeeper gives 15% discount and still makes 20% profit. Find the cost price.
Solution:
- SP = MP × (100 − 15)/100 = 1200 × 85/100 = ₹1,020
- CP = SP × 100/(100 + 20) = 1020 × 100/120 = ₹850
Answer: ₹850
Example 4: Successive Discounts
Find the single equivalent discount for successive discounts of 20% and 10%.
Solution:
- Equivalent discount = 20 + 10 − (20 × 10)/100
- = 30 − 2 = 28%
Answer: 28%
Example 5: Dishonest Dealer
A shopkeeper claims to sell rice at cost price but uses a weight of 900 gm instead of 1 kg. Find his profit percentage.
Solution:
- Profit % = [(1000 − 900) / 900] × 100
- = (100/900) × 100 = 11.11% or 100/9 %
Answer: 11.11% (or 11⅑%)
Common Mistakes
- Calculating profit % on SP instead of CP → Always remember: profit and loss percentages are calculated on Cost Price, not Selling Price.
- Applying discount on CP → Discount is always on Marked Price. First find SP using discount on MP, then compare with CP for profit/loss.
- Adding successive discounts directly → Two discounts of 20% and 10% do NOT equal 30%. Use the formula: d₁ + d₂ − (d₁ × d₂)/100.
- Confusing "profit on selling price" questions → Some tricky questions say "profit is 20% of SP." This is different from normal problems. Read carefully.
- Ignoring the base in dishonest dealer problems → The gain is calculated on the false weight (what dealer actually gives), not on the true weight.
- Assuming no loss when profit and loss percentages are equal → Selling two items at same profit% and loss% on same SP results in net loss = x²/100.
Quick Reference
- Profit % = (Profit/CP) × 100 — always on CP.
- SP with profit = CP × (100 + P%)/100
- SP with loss = CP × (100 − L%)/100
- SP after discount = MP × (100 − D%)/100
- Successive discounts a% and b% = a + b − ab/100
- Dishonest dealer gain = [(True − False)/False] × 100
- Equal profit & loss on same SP → Net loss = (%)²/100