Class 9 Mathematics Chapter 7 Comparing Quantities: Important Questions & Answers

Chapter 7 Comparing Quantities carries approximately 8–12 marks in the final board exam (split across 40-minute slots). The NCERT rationalization emphasizes problem-solving over memorization, meaning examiners prioritize questions that blend concepts—e.g., calculating discount followed by GST, or finding the rate of compound interest from a real-world scenario. The chapter tests four core competencies: (1) fluency with percentage and ratio conversions, (2) ability to distinguish and apply profit-loss and discount formulas correctly, (3) solving simple interest (SI) and compound interest (CI) word problems with time periods in months or years, and (4) interpreting financial data from tables or word statements. Board examiners expect you to show all working steps, not just final answers, especially for 3-mark and 5-mark questions. Many students lose marks by confusing profit% with profit amount, or by using SI formula for CI problems. This guide isolates each question type with fully worked solutions so you can identify and avoid these traps before your exam.

Multiple choice questions test concept recall and quick calculation. Each question is worth 1 mark; there are typically 2–4 MCQs on Comparing Quantities in the board exam. Read each option carefully and eliminate wrong answers systematically. **Q1.** If the marked price of an article is ₹500 and discount is 20%, then the selling price is: (a) ₹400 (b) ₹100 (c) ₹600 (d) ₹450 **Answer:** (a) ₹400 **Solution:** Discount = 20% of ₹500 = 0.20 × 500 = ₹100. Selling Price = Marked Price − Discount = 500 − 100 = ₹400. **Q2.** A person buys a cycle for ₹1200 and sells it for ₹1500. The profit percentage is: (a) 25% (b) 20% (c) 33.33% (d) 40% **Answer:** (a) 25% **Solution:** Profit = SP − CP = 1500 − 1200 = ₹300. Profit% = (Profit/CP) × 100 = (300/1200) × 100 = 25%. **Q3.** Simple interest on ₹2000 at 5% per annum for 2 years is: (a) ₹100 (b) ₹200 (c) ₹400 (d) ₹500 **Answer:** (b) ₹200 **Solution:** SI = (P × R × T)/100 = (2000 × 5 × 2)/100 = 20000/100 = ₹200. **Q4.** If 60% of a number is 120, the number is: (a) 72 (b) 180 (c) 200 (d) 240 **Answer:** (c) 200 **Solution:** Let the number be x. Then 0.60 × x = 120, so x = 120/0.60 = 200. **Q5.** The compound interest on ₹1000 at 10% per annum for 1 year (compounded annually) is: (a) ₹100 (b) ₹110 (c) ₹200 (d) ₹210 **Answer:** (a) ₹100 **Solution:** Amount = P(1 + R/100)ᵗ = 1000(1 + 10/100)¹ = 1000 × 1.10 = ₹1100. CI = Amount − Principal = 1100 − 1000 = ₹100.

Two-mark questions test basic application of formulas and straightforward two-step problems. Show clear working; one mark is often awarded for method, one for the correct answer. **Q1.** A shopkeeper buys shirts at ₹400 each and sells them at ₹480 each. Find his profit per shirt and profit percentage. **Answer:** Profit per shirt = SP − CP = 480 − 400 = ₹80. Profit% = (Profit/CP) × 100 = (80/400) × 100 = 20%. **Q2.** The price of an article is increased from ₹250 to ₹300. Find the percentage increase. **Answer:** Increase = 300 − 250 = ₹50. Percentage increase = (Increase/Original Price) × 100 = (50/250) × 100 = 20%. **Q3.** Find the simple interest on ₹5000 at 6% per annum for 3 years. **Answer:** SI = (P × R × T)/100 = (5000 × 6 × 3)/100 = 90000/100 = ₹900. **Q4.** A discount of 15% is given on an article marked at ₹800. What is the selling price? **Answer:** Discount = 15% of 800 = 0.15 × 800 = ₹120. Selling Price = 800 − 120 = ₹680. **Q5.** If 35% of a sum is ₹280, find the sum. **Answer:** Let the sum be x. Then 0.35x = 280, so x = 280/0.35 = ₹800.

Three-mark questions require multi-step reasoning, often combining two concepts (e.g., discount + profit, or SI + percentage). Write all steps clearly and label intermediate results. **Q1.** A merchant marks his goods 25% above the cost price. He then gives a discount of 10% on the marked price. Find his profit percentage. **Answer:** Let CP = ₹100 (assumed for simplicity). Marked Price = CP + 25% of CP = 100 + 25 = ₹125. Discount = 10% of MP = 0.10 × 125 = ₹12.50. Selling Price = MP − Discount = 125 − 12.50 = ₹112.50. Profit = SP − CP = 112.50 − 100 = ₹12.50. Profit% = (12.50/100) × 100 = 12.5%. **Q2.** The population of a town increases from 50,000 to 55,000 in one year. Find the percentage increase. If the population continues to increase at the same rate, what will be the population after 2 years? **Answer:** Year 1: Increase = 55,000 − 50,000 = 5,000. Percentage increase = (5000/50000) × 100 = 10%. Year 2: Population = 55,000 + 10% of 55,000 = 55,000 + 5,500 = ₹60,500. Alternatively, after 2 years: Population = 50,000(1.10)² = 50,000 × 1.21 = 60,500. **Q3.** A sum of money doubles itself in 4 years at simple interest. At what rate of interest per annum is it invested? **Answer:** Let Principal = P, then Amount = 2P (since it doubles). SI = A − P = 2P − P = P. Using SI = (P × R × T)/100: P = (P × R × 4)/100. Canceling P: 1 = (R × 4)/100, so R = 100/4 = 25% per annum. **Q4.** A shopkeeper purchased 100 pens at ₹5 each and 50 notebooks at ₹8 each. He sold all pens at ₹6 each and all notebooks at ₹10 each. Find his total profit and profit percentage on the whole transaction. **Answer:** CP of 100 pens = 100 × 5 = ₹500. CP of 50 notebooks = 50 × 8 = ₹400. Total CP = 500 + 400 = ₹900. SP of 100 pens = 100 × 6 = ₹600. SP of 50 notebooks = 50 × 10 = ₹500. Total SP = 600 + 500 = ₹1100. Total Profit = 1100 − 900 = ₹200. Profit% = (200/900) × 100 = 22.22% (approx).

Five-mark questions test deep conceptual understanding and require multi-step problem-solving, often with mixed concepts. Show every calculation step and reasoning. **Q1.** Ramesh invested ₹8000 at 5% per annum compound interest for 3 years. Calculate (a) the amount after 3 years, (b) the compound interest earned, and (c) explain the difference between simple interest and compound interest for this investment. **Answer:** (a) Amount after 3 years using A = P(1 + R/100)ᵗ: A = 8000(1 + 5/100)³ = 8000(1.05)³. Calculating: (1.05)³ = 1.05 × 1.05 × 1.05 = 1.157625. A = 8000 × 1.157625 = ₹9261. (b) Compound Interest = Amount − Principal = 9261 − 8000 = ₹1261. (c) For Simple Interest over 3 years: SI = (P × R × T)/100 = (8000 × 5 × 3)/100 = 120000/100 = ₹1200. Difference = CI − SI = 1261 − 1200 = ₹61. This difference exists because in CI, interest is calculated on interest earned in previous years (interest on interest), whereas SI is always calculated on the original principal only. **Q2.** A vendor buys apples at ₹20 per kg and sells them at a profit of 30%. However, he uses faulty weights and gives only 900 g when he claims to sell 1 kg. Calculate (a) the actual selling price per kg (based on what he actually gives), (b) the profit percentage on cost price, and (c) the profit earned per actual kg sold. **Answer:** (a) Marked/claimed selling price per kg = CP + 30% profit = 20 + 0.30 × 20 = 20 + 6 = ₹26 per kg (claimed). But he gives only 900 g for ₹26. Actual SP per kg (real weight) = (26/900) × 1000 = ₹28.89 (approx). (b) Actual Profit = Actual SP − CP = 28.89 − 20 = ₹8.89 per kg. Profit% = (8.89/20) × 100 = 44.44% (approx). Alternatively: For every 900 g sold, he charges ₹26, but CP of 900 g = 20 × (900/1000) = ₹18. Profit on 900 g = 26 − 18 = ₹8. Profit% = (8/18) × 100 = 44.44%. (c) Profit per actual kg sold = ₹8.89 (from part a) or calculated as: CP of 1 kg = ₹20; he gives only 900 g but charges ₹26, so profit = ₹26 − ₹18 = ₹8 per 900 g sold. Per kg: (8/900) × 1000 = ₹8.89. **Q3.** A bank offers two schemes for a deposit of ₹10,000: Scheme A at 8% simple interest per annum for 2 years, and Scheme B at 7% compound interest per annum for 2 years. Which scheme gives more return? By how much? **Answer:** Scheme A (Simple Interest): SI = (P × R × T)/100 = (10000 × 8 × 2)/100 = 160000/100 = ₹1600. Total Amount = 10000 + 1600 = ₹11,600. Scheme B (Compound Interest): Amount = P(1 + R/100)ᵗ = 10000(1 + 7/100)² = 10000(1.07)². (1.07)² = 1.1449. Amount = 10000 × 1.1449 = ₹11,449. CI = 11449 − 10000 = ₹1449. Comparison: Scheme A gives ₹11,600; Scheme B gives ₹11,449. Scheme A is better by ₹11,600 − ₹11,449 = ₹151. Conclusion: Despite a lower rate, Scheme A's simple interest for 2 years yields more than Scheme B's compound interest for 2 years in this case.

**Case Study Question:** A mobile phone manufacturing company offers the following promotional scheme to its retailers: • On purchase of phones costing ₹20,000 and above, the retailer gets a 15% trade discount. • On the final amount after trade discount, an additional 5% is offered if the retailer buys in bulk (10 or more units). • GST at 12% is applicable on the final discounted price. A retailer buys 12 phones at ₹20,000 each. **(a) Calculate the total amount the retailer must pay (including GST).** **Step 1 (Trade Discount):** Marked Price (MP) of 12 phones = 12 × 20,000 = ₹2,40,000. Trade Discount = 15% of MP = 0.15 × 2,40,000 = ₹36,000. Price after trade discount = 2,40,000 − 36,000 = ₹2,04,000. **Step 2 (Bulk Discount):** Bulk Discount (additional 5%) = 5% of 2,04,000 = 0.05 × 2,04,000 = ₹10,200. Price after bulk discount = 2,04,000 − 10,200 = ₹1,93,800. **Step 3 (GST):** GST = 12% of 1,93,800 = 0.12 × 1,93,800 = ₹23,256. Final Amount = 1,93,800 + 23,256 = ₹2,17,056. **(b) If the retailer sells each phone at ₹24,000, calculate his profit percentage.** **Cost Price for retailer = 2,17,056/12 = ₹18,088 per phone (approx).** Selling Price = ₹24,000 per phone. Profit per phone = 24,000 − 18,088 = ₹5,912. Profit% = (5,912/18,088) × 100 = 32.68% (approx). **(c) The retailer claims that after giving a discount of 8% to his customers, he still makes a 20% profit. Verify this claim.** **Expected SP with 20% profit = CP × 1.20 = 18,088 × 1.20 = ₹21,705.60.** Actual SP after 8% discount = 24,000 − (8% of 24,000) = 24,000 − 1,920 = ₹22,080. Since ₹22,080 > ₹21,705.60, the claim is **TRUE**. The retailer makes more than 20% profit even after the 8% discount.

CBSETUTOR.ai's AI-powered mathematics tutoring engine is designed specifically to help Class 9 students master Comparing Quantities through daily, adaptive drilling. Here's how our platform reinforces these exact question types: **Personalized Problem Generation:** Our AI generates unlimited variations of profit-loss, discount, and interest problems tailored to your performance level. If you struggle with compound interest calculations, the system automatically increases CI problem frequency and scaffolds explanations step-by-step. **Real-Time Error Analysis:** When you solve a question, the AI doesn't just mark it wrong—it identifies *why* you made the error. Common mistakes like confusing profit% with profit amount, or forgetting GST in discount problems, trigger targeted micro-lessons that clarify the concept in seconds. **Spaced Repetition with Context:** Instead of solving 50 similar questions at once, CBSETUTOR.ai spaces your practice strategically. After you solve a 5-mark CI problem, the system waits 2–3 days, then presents a slightly harder variant. This spacing strengthens long-term retention and prevents cramming fatigue. **Step-by-Step Solution Walkthroughs:** Every question in our system includes annotated, line-by-line solutions. When you're stuck, you can unlock hints progressively (formula reminder → first step → full solution), so you always learn, never just copy. **Mock Exam Simulations:** CBSETUTOR.ai hosts full Chapter 7 mock tests that mirror the exact 2024-25 board pattern: 1-mark MCQs, 2-mark shorts, 3-mark analyticals, and 5-mark case studies, all timed. Your score report identifies weak areas so you can focus revision efficiently. **Parent Dashboard:** Parents receive weekly progress summaries showing which question types their child has mastered and where gaps remain—enabling informed support at home.