Profit & Loss - All Formulas & Shortcuts

Quick reference guide for all Profit & Loss formulas with instant calculation tricks

📘 Basic Formulas

1. Core Definitions

Cost Price (CP) = Price at which article is purchased Selling Price (SP) = Price at which article is sold Marked Price (MP) = Price marked on the article Discount = Reduction on Marked Price

2. Profit & Loss Formulas

Profit:

Profit = SP - CP (when SP > CP) Profit% = (Profit/CP) × 100 Profit% = [(SP - CP)/CP] × 100

Loss:

Loss = CP - SP (when CP > SP) Loss% = (Loss/CP) × 100 Loss% = [(CP - SP)/CP] × 100

Key Point: Profit% and Loss% are ALWAYS calculated on Cost Price (CP)

3. Finding SP from CP and Profit/Loss%

When Profit% is given:

SP = CP(1 + Profit%/100) OR SP = CP × (100 + Profit%)/100

When Loss% is given:

SP = CP(1 - Loss%/100) OR SP = CP × (100 - Loss%)/100

Quick Examples:

• CP = 500, Profit = 20% → SP = 500 × 1.2 = 600
• CP = 800, Loss = 10% → SP = 800 × 0.9 = 720

4. Finding CP from SP and Profit/Loss%

When Profit% is given:

CP = SP × 100/(100 + Profit%) OR CP = SP/(1 + Profit%/100)

When Loss% is given:

CP = SP × 100/(100 - Loss%) OR CP = SP/(1 - Loss%/100)

Quick Examples:

• SP = 600, Profit = 20% → CP = 600 × 100/120 = 500
• SP = 720, Loss = 10% → CP = 720 × 100/90 = 800

🎯 Discount Formulas

5. Basic Discount Formulas

Discount:

Discount = MP - SP Discount% = (Discount/MP) × 100

Finding SP from MP and Discount%:

SP = MP(1 - Discount%/100) OR SP = MP × (100 - Discount%)/100

Relation between MP, CP, Profit, Discount:

SP = MP - Discount SP = CP + Profit Therefore: MP - Discount = CP + Profit

6. Successive Discounts

Two successive discounts d₁% and d₂%:

Total Discount% = d₁ + d₂ - (d₁ × d₂)/100

Example: 20% + 10% successive discounts

Total = 20 + 10 - (20 × 10)/100 = 30 - 2 = 28%

Final Price after successive discounts:

Final SP = MP × (1 - d₁/100) × (1 - d₂/100)

Three successive discounts:

Final SP = MP × (1 - d₁/100) × (1 - d₂/100) × (1 - d₃/100)

⚡ Quick Shortcuts

7. Two Articles at Same SP

One sold at x% profit, other at x% loss:

If SP is same for both:

Overall Result = ALWAYS LOSS Loss% = (x/10)²

Example: One at 20% profit, other at 20% loss

Loss% = (20/10)² = 4% = 4% loss

Memory Trick: “Same SP, same %, always loss of (x/10)²”

8. Finding Profit% when articles sold

If selling price of x articles = Cost price of y articles:

Profit% = [(y - x)/x] × 100

Example: SP of 5 articles = CP of 6 articles

Profit% = [(6-5)/5] × 100 = 20%

Loss occurs when y < x

9. Dishonest Dealer Formulas

Dealer claims to sell at CP but uses false weight:

If uses x grams instead of 1000 grams:

Profit% = [(1000 - x)/x] × 100

Example: Uses 900g instead of 1000g

Profit% = [(1000-900)/900] × 100 = 11.11%

If dealer gives x% less weight:

Profit% = [x/(100-x)] × 100

10. When article sold at x% loss instead of y% profit

Difference in SP = Actual difference given

CP = (Actual Difference × 100)/(x + y)

Example: If sold at 10% loss instead of 15% profit, loss = ₹500

CP = (500 × 100)/(10 + 15) = 50000/25 = ₹2000

🔥 Advanced Tricks

11. Break-Even Point

When to mix profit and loss items:

If x articles give p% profit, y articles give l% loss:

x/y = l/p (for no profit no loss)

Example: Some at 20% profit, some at 10% loss (breakeven)

Ratio = 10/20 = 1/2 = 1:2

12. Marked Price when Profit% and Discount% given

Given: CP, Profit%, Discount%

Method:

SP = CP(1 + Profit%/100) MP = SP/(1 - Discount%/100)

Direct Formula:

MP = CP × (100 + Profit%)/(100 - Discount%)

Example: CP = 500, Profit = 20%, Discount = 10%

MP = 500 × 120/90 = 500 × 4/3 = ₹666.67

13. Finding CP when MP and both Discount% and Profit% are given

CP = MP × (100 - Discount%)/(100 + Profit%)

14. Overall Profit/Loss with Multiple Items

Total Profit/Loss %:

Overall % = (Total Profit or Loss / Total CP) × 100

Shortcut when quantities are same:

• Buy at average CP
• Sell at average SP
• Calculate profit/loss on average

💡 Exam-Specific Patterns

Pattern 1: False Balance

Dealer uses x grams for 1 kg and sells at y% profit:

Total Gain% = [(1000-x)/x + y] × 100

Pattern 2: Selling at Cost Price after Mixing

Mix cheap item (CP₁) with costly item (CP₂):

To sell at CP₂ without loss:

Ratio = (CP₂ - CP_mix) : (CP_mix - CP₁)

Pattern 3: Partnership in Profit

If A invests a, B invests b:

Profit share ratio = a:b (if time is same)

If different time periods:

Ratio = (a × t₁):(b × t₂)

Pattern 4: Markup on Cost

Markup% = Percentage over CP

MP = CP(1 + Markup%/100)

After discount d% on MP, profit p%:

(100 + p) = (100 + Markup)(100 - d)/100

🎓 Mental Math Techniques

Trick 1: Quick Profit% Calculation

If CP = 100:

• SP = 120 → Profit = 20%
• SP = 90 → Loss = 10%

If CP ≠ 100: Scale it

• CP = 500, SP = 600
• Scale to: CP = 100, SP = 120 (divide by 5)
• Profit = 20%

Trick 2: Finding CP Instantly

SP = 660, Profit = 10%

Method:

CP = 660/1.1 = 600

For 20% profit:

CP = SP/1.2

For 25% profit:

CP = SP/1.25 = SP × 4/5

Trick 3: Two Discounts vs Single Discount

20% + 10% successive = ?

Quick:

• First: 80% remains
• Second: 90% of 80% = 72%
• Total discount = 28%

OR use formula: 20 + 10 - 2 = 28%

Trick 4: Common Profit% Values

CP	SP	Profit%
100	110	10%
100	120	20%
100	125	25%
100	150	50%
100	200	100%
80	100	25%
75	100	33.33%
50	100	100%

📊 Quick Reference Table

CP to SP Multipliers

SP to CP Dividers

🎯 Golden Rules

1. Always calculate Profit/Loss% on CP (not SP or MP)
2. Successive discounts: Use formula, never add directly
3. Same SP, same % profit/loss: Always results in loss
4. Dishonest dealer: Profit even when selling at CP
5. Check answer: If profit, SP > CP; if loss, SP < CP

💎 Common Mistakes to Avoid

❌ Calculating profit% on SP instead of CP ❌ Adding successive discounts directly (20% + 10% ≠ 30%) ❌ Forgetting that MP ≠ SP when discount is given ❌ Using wrong formula for reverse calculation ✅ Always identify what is given: CP, SP, MP, Profit%, Loss%, Discount%

🔗 Related Resources

Practice Questions:

• Profit & Loss Practice Questions

Theory:

• Profit & Loss Theory & Concepts

Related Topics:

• Percentage
• Discount
• Simple Interest

Study Resources:

• All-in-One Formula Sheet
• Shortcuts & Tricks

Master these formulas and solve P&L questions in 45 seconds! ⚡