Class 9 Mathematics Chapter 7 Comparing Quantities: Previous Year Questions (2020–2025)

Most students approach Chapter 7 by memorising formulas: Profit = SP – CP, Discount % = (Discount / MP) × 100, A = P(1 + r/100)ⁿ. Then they open a question paper and freeze. Why? Because past papers don't test formula recall—they test reasoning under pressure. A real CBSE question might ask: 'A shopkeeper marks goods at 25% above cost. He offers 10% discount. What is his profit %?' The formula isn't the barrier; identifying that profit is on CP, not MP, is. When you solve 5–10 variations of this setup, your brain builds pattern recognition. You start spotting red flags: 'Is the rate per annum or per half-year?' 'Is 15% gain on cost price or selling price?' Past papers also expose syllabus gaps. Many Class 9 students skip ratio simplification or percentage-to-fraction conversion—both vital here. A 1-mark question like 'Express 5:7 as a percentage' reveals if you know 5/(5+7) × 100 = 41.67%. Working 10 such papers reveals exactly what to revise, saving 5 hours of aimless study. Additionally, past papers normalise question types: the 'successive discount' problem, the 'amount after 2 years at compound interest', the 'loss percentage disguised as profit'. You stop panicking and start solving methodically.

1-mark questions in Comparing Quantities test speed and conceptual clarity. These five are variations seen repeatedly: **Q1: A man buys a pen for ₹25 and sells it for ₹30. Find his profit percentage.** Answer: Profit = 30 – 25 = ₹5. Profit % = (5/25) × 100 = 20%. **Q2: If the cost price of 10 pens is ₹100, find the cost price of 1 pen.** Answer: CP of 1 pen = 100/10 = ₹10. **Q3: A shirt is marked at ₹500. A discount of 20% is given. What is the selling price?** Answer: Discount = 20% of 500 = 100. SP = 500 – 100 = ₹400. **Q4: Express 3:4 as a percentage.** Answer: 3/(3+4) × 100 = 3/7 × 100 ≈ 42.86%. **Q5: Simple interest on ₹1000 for 2 years at 5% p.a. is ___.** Answer: SI = (1000 × 5 × 2) / 100 = ₹100. Key insight: These questions reward accuracy in ratio basics and formula application. Most errors stem from wrong order of operations or confusing 'profit on CP' with 'profit on SP'. Practise these 20 times to build speed.

3-mark questions demand multi-step reasoning and clear communication. Examiners mark 1 point for approach, 1 for calculation, 1 for final answer. **Q1: A tradesman marks his goods 30% above cost price and allows a discount of 10%. Find his gain or loss percentage.** Solution: Let CP = ₹100. MP = 100 + 30% of 100 = ₹130. Discount = 10% of 130 = ₹13. SP = 130 – 13 = ₹117. Gain = 117 – 100 = ₹17. Gain % = (17/100) × 100 = 17%. ✓ **Q2: Find the amount on ₹2000 for 2 years at 5% p.a. compound interest, compounded annually.** Solution: A = P(1 + r/100)ⁿ = 2000(1 + 5/100)² = 2000(1.05)² = 2000 × 1.1025 = ₹2205. ✓ **Q3: If 20% of x is 240, find x.** Solution: 20% of x = 240 → (20/100) × x = 240 → x = 240 × (100/20) = ₹1200. ✓ **Q4: The price of a book increases from ₹150 to ₹180. Find the percentage increase.** Solution: Increase = 180 – 150 = ₹30. % increase = (30/150) × 100 = 20%. ✓ **Q5: A man invests ₹5000 at 8% p.a. simple interest. How much will he have after 3 years?** Solution: SI = (5000 × 8 × 3) / 100 = ₹1200. Total = 5000 + 1200 = ₹6200. ✓ Pattern: All involve two operations (markup → discount, or principal → interest). Avoid sign errors (gain vs. loss). Always check: is the percentage on the original or derived quantity?

5-mark questions combine 2–3 sub-concepts and expect detailed working. These are the marks that separate 70 from 85. **Q1: A shopkeeper buys 400 mangoes at ₹10 per dozen. He sells 200 at ₹1.25 each and 150 at ₹1 each. The rest are sold at 50 paise each. Find his overall profit or loss percentage.** Solution: Cost Price: 400 mangoes = 400/12 dozen = 33⅓ dozen. CP = 33⅓ × 10 = ₹333.33. Selling Price: 200 at ₹1.25 each = ₹250. 150 at ₹1 each = ₹150. Remaining = 400 – 200 – 150 = 50. 50 at ₹0.50 each = ₹25. Total SP = 250 + 150 + 25 = ₹425. Profit = 425 – 333.33 = ₹91.67. Profit % = (91.67/333.33) × 100 ≈ 27.5%. ✓ **Q2: Rahul borrows ₹8000 from a bank at 12% p.a. compound interest. How much must he pay after 2 years? If he pays ₹2000 after 1 year, how much does he owe after 2 years?** Solution (without intermediate payment): A = 8000(1.12)² = 8000 × 1.2544 = ₹10,035.20. With ₹2000 paid after 1 year: After 1 year, Amount = 8000 × 1.12 = ₹8960. After payment: 8960 – 2000 = ₹6960. After 2nd year: 6960 × 1.12 = ₹7795.20. ✓ **Q3: A property worth ₹50,000 depreciates at 10% per annum. Find its value after 3 years. Also find the total depreciation.** Solution: Value after 3 years = 50,000(1 – 10/100)³ = 50,000(0.9)³ = 50,000 × 0.729 = ₹36,450. Total depreciation = 50,000 – 36,450 = ₹13,550. Depreciation % = (13,550/50,000) × 100 = 27.1%. ✓ Key: Show all steps. Examiners award partial credit if method is sound but arithmetic slips. Always write the formula first.

The rationalized 2024–25 CBSE syllabus removed some applications but deepened conceptual rigour. Emerging patterns for 2026–27: 1. **Emphasis on Real-World Contexts**: Questions increasingly embed profit-loss in GST scenarios or investment apps. Expect: 'A company offers 5% cashback on ₹1000 purchase. GST is 12%. Calculate final cost.' Two-step percentage problems will dominate. 2. **Compound Interest Over Simple**: SI questions remain, but CI increasingly appears in 5-mark slots with sub-parts (e.g., find amount, then find total interest, then compare with SI). 3. **Ratio Simplification as a Skill**: Rather than standalone 'simplify 15:25', expect 'If A:B = 3:4 and B:C = 2:5, find A:C'. Transitive ratio reasoning is tested. 4. **Less Rote, More Reasoning**: 'A shopkeeper marks at X% above CP and gives Y% discount. Explain whether he makes profit or loss.' Open-ended justification answers are creeping into 5-mark slots. 5. **Calculator-Free Constraint**: Exams remain non-calculator. Expect 'clean' numbers: 5%, 10%, 20%, 25%, 50% rather than 7.5% or 13%. But approximations like (1.05)² = 1.1025 must be computed by hand. 6. **Absence of Complex SI Formulae**: Class 10 covers SI with varying rates; Class 9 sticks to constant rate. Don't memorise beyond A = P + SI and A = P(1 + r/100)ⁿ. Strategy: Focus on conceptual clarity, not formula collection. A student who understands why CP is the base for profit % will solve any variant.

During an exam, panic ruins accuracy. Use this sequence: **Step 1: Identify the Base (60 seconds).** Read the question twice. Underline: Is percentage on CP, MP, SP, or original amount? Mark it. Example: 'Profit of 20%' → base is CP. 'Discount of 15%' → base is MP. 'Amount after 2 years' → base is Principal. **Step 2: Set Values (90 seconds).** If numbers are awkward, assume CP = 100 or Principal = 100. If given specific values, use them but write them clearly. Example: Given: MP = ₹500, Discount = 20%. Discount amount = 0.20 × 500 = ₹100. SP = 500 – 100 = ₹400. **Step 3: Apply Formula (120 seconds).** Write the formula before substituting. Profit % = [(SP – CP) / CP] × 100. Then plug numbers. Never skip the formula line—examiners award marks for method even if calculation errs. **Step 4: Sanity Check (30 seconds).** Does the answer make sense? Profit % should be positive if SP > CP. Discount can't exceed 100%. Interest should grow with time. If your answer fails basic logic, recalculate. **For 5-Mark Questions: Allocate 5 minutes.** 60 seconds reading, 120 seconds per sub-part (usually 2–3 sub-parts), 60 seconds review. **Common Pitfalls to Avoid:** - Confusing 'loss of 10%' with '10% reduction' (they're the same; don't double-count). - Forgetting 'per annum' in interest rates (always annualise). - Applying discount to CP instead of MP. - Using simple interest formula for compound interest. Start a 3-day free trial at cbsetutor.ai to get unlimited past-paper practice with AI-instant feedback on each working step.

**Q: Is profit always calculated on cost price in Class 9?** A: Yes, unless explicitly stated otherwise. Profit % = [(SP – CP) / CP] × 100. Always divide by the cost, not selling price. **Q: What's the difference between markup and profit?** A: Markup is how much above CP you price the item (MP = CP + markup). Profit is what you actually gain after discount (Profit = SP – CP). A 30% markup doesn't guarantee 30% profit if you discount. **Q: When is compound interest calculated half-yearly?** A: The question will explicitly say 'compounded half-yearly' or 'compounded quarterly'. Default is annual. If half-yearly, divide rate by 2 and double the time period. Example: 8% p.a. compounded half-yearly for 1 year = 4% for 2 half-years. **Q: How do I compare ratios like 3:5 and 4:7?** A: Convert to fractions: 3/5 vs 4/7. Find LCD: 3/5 = 21/35, 4/7 = 20/35. So 3:5 > 4:7. **Q: Can loss percentage be more than 100%?** A: No. Maximum loss is 100% (when SP = 0). In Class 9 problems, expect loss % between 0–50%. **Q: Is 'discount' always subtracted from marked price?** A: Yes. SP = MP – (Discount % of MP). Never apply discount to CP. **Q: How many decimal places should I round to?** A: Unless stated, round currency to 2 decimal places (paise) and percentages to 1–2 decimal places. Write ₹15.50, not ₹15.50000.