Class 9 Mathematics Chapter 7 Comparing Quantities MCQ with Answers – Complete Quiz

The reformed CBSE Class 9 Mathematics question paper now allocates 20–25 marks to objective questions (MCQs and short-answer hybrids). Chapter 7 Comparing Quantities contributes 4–5 MCQs in the typical blueprint, and the trend is upward. Why? MCQs test conceptual clarity faster than long-form answers. In Comparing Quantities, examiners can pack a single MCQ with multiple concepts: 'A shopkeeper marked goods at 150% of cost price, offered 20% discount, and earned 8% profit. What is the cost price?' — this single question combines markup, discount, and profit percentage simultaneously. Without a systematic understanding of ratio, percentage conversion (how 20% discount translates to 0.8 multiplier), and profit formula, students pick wrong answers. The new CBSE pattern rewards speed + accuracy. Assertion–Reason MCQs (where two statements are given and you verify if one explains the other) are increasingly common in Class 9 boards. Mastering these question types early builds the logical thinking needed for Class 10 and beyond. This guide decodes the pattern, shows you where shortcuts work, and where they fail.

**Q1.** If the ratio of two numbers is 3:5 and their sum is 56, what is the larger number? (A) 21 (B) 35 (C) 28 (D) 42 **Answer:** (B) 35 **Reason:** If ratio is 3:5, numbers are 3x and 5x. Sum = 3x + 5x = 8x = 56 ⟹ x = 7. Larger = 5(7) = 35. **Q2.** A T-shirt costs ₹400. Its price increases by 15%. What is the new price? (A) ₹415 (B) ₹460 (C) ₹575 (D) ₹385 **Answer:** (B) ₹460 **Reason:** New price = 400 + 15% of 400 = 400(1.15) = ₹460. **Q3.** If cost price = ₹500 and selling price = ₹600, what is the profit percentage? (A) 25% (B) 20% (C) 16.67% (D) 10% **Answer:** (B) 20% **Reason:** Profit = 600 − 500 = 100. Profit% = (100/500) × 100 = 20%. **Q4.** A discount of 10% is offered on ₹800. What is the discounted price? (A) ₹720 (B) ₹880 (C) ₹790 (D) ₹710 **Answer:** (A) ₹720 **Reason:** Discounted price = 800 − 10% of 800 = 800(0.9) = ₹720. **Q5.** Simple interest on ₹1000 for 2 years at 5% per annum is: (A) ₹50 (B) ₹100 (C) ₹200 (D) ₹1050 **Answer:** (B) ₹100 **Reason:** SI = (P × R × T)/100 = (1000 × 5 × 2)/100 = ₹100. **Q6.** If a shirt is sold at a loss of 15%, and cost price is ₹800, the selling price is: (A) ₹680 (B) ₹920 (C) ₹750 (D) ₹1000 **Answer:** (A) ₹680 **Reason:** SP = CP × (1 − loss%) = 800(0.85) = ₹680. **Q7.** What is 35% of 400? (A) 120 (B) 140 (C) 160 (D) 180 **Answer:** (B) 140 **Reason:** 35% of 400 = 0.35 × 400 = 140. **Q8.** The ratio of 2 hours to 30 minutes in simplest form is: (A) 2:30 (B) 4:1 (C) 1:4 (D) 60:30 **Answer:** (B) 4:1 **Reason:** 2 hours = 120 minutes. Ratio = 120:30 = 4:1 (divide by 30). **Q9.** If compound interest for 1 year at 10% p.a. on ₹500 is calculated, what is the amount? (A) ₹550 (B) ₹525 (C) ₹600 (D) ₹510 **Answer:** (A) ₹550 **Reason:** For 1 year, CI = SI. Amount = 500(1 + 0.1) = ₹550. **Q10.** A number is increased by 20% and then decreased by 10%. What is the overall percentage change? (A) 10% increase (B) 8% increase (C) 10% decrease (D) 12% decrease **Answer:** (B) 8% increase **Reason:** Take initial number = 100. After 20% increase = 120. After 10% decrease = 120(0.9) = 108. Overall change = 8% increase.

**Q11.** A merchant marks goods at 40% above cost price and offers a 20% discount. What is the profit percentage? (A) 20% (B) 12% (C) 8% (D) 15% **Answer:** (B) 12% **Reason:** Let CP = 100. Marked price = 140. After 20% discount, SP = 140(0.8) = 112. Profit% = (112 − 100)/100 × 100 = 12%. **Q12.** Compound interest on ₹5000 for 2 years at 8% p.a. is: (A) ₹800 (B) ₹832 (C) ₹850 (D) ₹900 **Answer:** (B) ₹832 **Reason:** Amount = 5000(1 + 0.08)² = 5000(1.1664) = ₹5832. CI = 5832 − 5000 = ₹832. **Q13.** A shopkeeper buys goods at ₹60 per unit and sells at ₹75 per unit. If overhead costs are ₹300, and he sells 50 units, what is the net profit? (A) ₹450 (B) ₹350 (C) ₹600 (D) ₹550 **Answer:** (A) ₹450 **Reason:** Total gain = (75 − 60) × 50 = 15 × 50 = ₹750. Net profit = 750 − 300 = ₹450. **Q14.** If the price of rice increases from ₹40 per kg to ₹50 per kg, what is the percentage increase? (A) 20% (B) 25% (C) 22.5% (D) 10% **Answer:** (B) 25% **Reason:** Increase = 50 − 40 = 10. % increase = (10/40) × 100 = 25%. **Q15.** A person invests ₹8000 for 3 years at 10% per annum simple interest. What is the amount after 3 years? (A) ₹10,400 (B) ₹10,000 (C) ₹9,200 (D) ₹12,000 **Answer:** (A) ₹10,400 **Reason:** SI = (8000 × 10 × 3)/100 = ₹2400. Amount = 8000 + 2400 = ₹10,400. **Q16.** If a book is sold at ₹240 with a profit of 20%, what was the cost price? (A) ₹180 (B) ₹288 (C) ₹200 (D) ₹220 **Answer:** (C) ₹200 **Reason:** SP = CP(1 + profit%). 240 = CP(1.2) ⟹ CP = 240/1.2 = ₹200. **Q17.** Two quantities are in the ratio 7:3. If their sum is 200, what is the difference? (A) 80 (B) 120 (C) 70 (D) 100 **Answer:** (A) 80 **Reason:** Let quantities be 7x and 3x. Sum = 10x = 200 ⟹ x = 20. Quantities are 140 and 60. Difference = 140 − 60 = 80. **Q18.** A suit marked at ₹5000 is sold at ₹4200. What is the discount percentage? (A) 18% (B) 20% (C) 16% (D) 22% **Answer:** (C) 16% **Reason:** Discount = 5000 − 4200 = 800. Discount% = (800/5000) × 100 = 16%. **Q19.** What rate of simple interest is needed to earn ₹600 on ₹1000 in 3 years? (A) 15% (B) 18% (C) 20% (D) 25% **Answer:** (C) 20% **Reason:** SI = (P × R × T)/100. 600 = (1000 × R × 3)/100 ⟹ R = 20%. **Q20.** A student scores 70% in one exam and 85% in another. If both exams have equal weight, what is the average percentage? (A) 77.5% (B) 78% (C) 80% (D) 75% **Answer:** (A) 77.5% **Reason:** Average = (70 + 85)/2 = 155/2 = 77.5%.

**Q21.** **Assertion (A):** If a man buys 100 items at ₹5 each and sells them at ₹7.50 each, his profit is 50%. **Reason (R):** Profit% = (SP − CP)/CP × 100. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** CP = 500, SP = 750. Profit = 250. Profit% = (250/500) × 100 = 50%. R is the correct formula, so it explains A. **Q22.** **Assertion (A):** When a price is reduced by 20%, then by 10%, the overall reduction is 30%. **Reason (R):** Successive percentage changes are not additive; multiply multipliers instead. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (D) A is false, R is true **Reason:** Overall reduction = (0.8 × 0.9) − 1 = 0.72 − 1 = −0.28 = 28%, not 30%. R is correct. **Q23.** **Assertion (A):** Compound interest for 2 years at 5% p.a. on ₹1000 is ₹102.50. **Reason (R):** CI = P[(1 + r)ⁿ − 1]. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** CI = 1000[(1.05)² − 1] = 1000[1.1025 − 1] = 1000(0.1025) = ₹102.50. R is the correct formula. **Q24.** **Assertion (A):** A shopkeeper gains 30% by selling a shirt at ₹325, so the cost price was ₹250. **Reason (R):** If gain is 30%, then SP = CP × 1.3. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** 325 = CP × 1.3 ⟹ CP = 250. R provides the correct relationship, explaining A. **Q25.** **Assertion (A):** If the marked price of an item is ₹1000 and a customer gets two successive discounts of 20% and 10%, the final price is ₹700. **Reason (R):** Successive discounts are applied multiplicatively: Final = MP × (1 − d₁) × (1 − d₂). (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** Final = 1000 × 0.8 × 0.9 = 1000 × 0.72 = ₹720, not ₹700. So A is false, R is true. **Correction:** A is false, R is true → Answer is (D). **Q26.** **Assertion (A):** A man lends ₹10,000 at 6% p.a. simple interest for 2 years. The amount returned is ₹11,200. **Reason (R):** SI = (P × R × T)/100; Amount = P + SI. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** SI = (10000 × 6 × 2)/100 = 1200. Amount = 10000 + 1200 = ₹11,200. R is the correct method. **Q27.** **Assertion (A):** If the ratio of boys to girls in a class is 5:3, and there are 24 girls, then there are 40 boys. **Reason (R):** In a ratio a:b, if one part = x, the actual value = (actual value of known part / ratio part) × ratio part of unknown. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** If ratio is 5:3 and girls = 24, then 3 units = 24 ⟹ 1 unit = 8. Boys = 5 × 8 = 40. R explains the method correctly. **Q28.** **Assertion (A):** A person buys shares at ₹100 each, sells 60% at ₹120, and 40% at ₹90. The overall loss is 2%. **Reason (R):** Overall profit/loss% = (Total SP − Total CP) / Total CP × 100. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** Assume 100 shares. CP = 10,000. SP = 60(120) + 40(90) = 7200 + 3600 = 10,800. Gain = 8%, not loss. A is false, R is true → Answer is (D). **Q29.** **Assertion (A):** If a car is bought for ₹5,00,000 and depreciates at 10% per annum, its value after 2 years is ₹4,05,000. **Reason (R):** Depreciation over time uses the compound formula: Value = P(1 − r)ⁿ. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** Value = 500000(0.9)² = 500000(0.81) = ₹405,000. R is the correct depreciation formula. **Q30.** **Assertion (A):** If the cost price of 12 pens is ₹60, and the selling price of 10 pens is ₹60, the loss percentage is 20%. **Reason (R):** Loss% = (CP − SP) / CP × 100, calculated per unit. (A) Both A and R are true, R explains A (B) Both A and R are true, R does not explain A (C) A is true, R is false (D) A is false, R is true **Answer:** (A) Both A and R are true, R explains A **Reason:** CP per pen = 5, SP per pen = 6. No loss; gain of 20%. A is false, R is true → Answer is (D).

**1. Additive vs. Multiplicative Confusion:** The most common trap in Comparing Quantities is treating successive changes (discounts, interest, depreciation) additively instead of multiplicatively. Example: 'A 20% discount followed by a 10% discount equals a 30% discount.' This is WRONG. Correct: (0.8 × 0.9 − 1) × 100 = 28% discount. Many exam options include 30% to catch unprepared students. **2. Loss of Precision in Percentages:** Options often include slightly wrong values like ₹102 instead of ₹102.50 for CI, or 20.5% instead of 20%. Verify your calculation to 2 decimal places, especially in compound interest questions. **3. Forgetting the Base Change:** In profit/loss questions, students calculate profit% on selling price instead of cost price. Example: 'If SP = ₹120 and profit = ₹20, profit% = 20/120 × 100 = 16.67%' (WRONG). Correct: 20/100 × 100 = 20% (base is CP = 100). Options exploit this error. **4. Ratio Simplification Errors:** A ratio 120:30 should simplify to 4:1, not 2:1. Examiners include the unsimplified form or wrong simplification as traps. Always divide by the GCD. **5. Mismatched Units in Ratios:** Converting hours to minutes or days to hours before forming ratios is crucial. '2 hours to 30 minutes' trap: forgetting to convert 2 hours = 120 minutes leads to ratio 2:30, which is then wrongly 'simplified' to 1:15 instead of 4:1. **6. SI vs. CI Confusion:** In 1 year, SI = CI, but students often select different values due to rounding errors in compound interest calculations. Always verify that for n = 1, Amount (CI) − P = SI. **7. Marked Price vs. Cost Price:** 'A shopkeeper marks at 40% above CP.' Many students confuse markup (on CP) with discount (on MP). Correct: MP = CP × 1.4, then discount is applied to MP, not CP. **8. Percentage vs. Percentage Points:** 'Profit increased from 20% to 30%' means a 50% relative increase in profit, not a 10 percentage-point increase. Options blur this distinction intentionally. **9. Discount on Marked vs. List Price:** Always clarify: is 20% discount on marked price or original price? The problem statement matters. Blind option selection fails here.

**Read-Solve-Verify Cycle (2.5 min/question):** With 30 MCQs in 75–90 minutes (mock exam format), you have ~2.5 minutes per question on average. Allocate: 1 min reading, 1 min solving, 30 sec verification. This prevents careless errors. For easy MCQs (Q1–10), aim for 1.5 min each; medium (Q11–20), 2.5 min; hard assertion–reason (Q21–30), 3–3.5 min. **Estimation First, Exact Later:** Before calculating, estimate the answer's magnitude. If profit% should be around 10–15%, and an option shows 50%, eliminate it immediately. This halves the field and saves time. For compound interest, rough approximations (Sn ≈ P[1 + nr + (n(n-1)/2)r²]) can validate without full calculation. **Assertion–Reason Triage:** Read the Reason (R) first. If R is false, the answer is (C) or (D) regardless of A. This saves mental effort. Then verify if R logically supports A (does R explain the 'why' of A?), or if both are true but unrelated (answer B). **Check Dimension/Unit Consistency:** A quick scan prevents magnitude errors. If the question is about profit in rupees and an option is a percentage, it's a decoy. If time is involved and you forgot to convert units, re-examine immediately. **Work Backwards from Options (When Stuck):** For ratio and profit questions, substituting small option values (e.g., CP = 200) is faster than deriving algebraically. If A is ₹180, B is ₹200, C is ₹220, test B (middle value) first in the SP = CP(1.2) relationship. **Avoid Second-Guessing After Verification:** Once you've verified an answer using the correct formula, do not change it under time pressure. Exam anxiety leads to flip-flopping. Document your method in a side margin (yes, write rough work) to trace errors post-exam. **Flag 'Percent of Percent' Questions:** Phrases like 'A is 20% more than B, and B is 10% less than C' require careful parsing. Convert each to a multiplier (1.2 for +20%, 0.9 for −10%) and multiply. Many students add percentages, triggering the trap. **In Assertion–Reason, Assume Independence First:** Do not assume R will always support A. Many questions pair true-but-unrelated statements. Read carefully to determine if the logical link exists. This mindset prevents option-jumping.

You now have 30 authentic CBSE-aligned MCQ questions spanning Comparing Quantities' full scope: ratio & percentage fundamentals, profit & loss with markup/discount, and compound interest over multiple years. The progression from easy (direct formula application) to hard (multi-step scenarios + assertion–reason logic) mirrors actual board exams. The trap options dissected above are not theoretical—they appear consistently in JEE Foundation exams and CBSE board papers. Studying this guide isn't a one-time activity. Revisit questions you got wrong, focus on the 'Reason' field, and redrive the entire quiz after 3 days. Time yourself. Aim for 27/30 (90%) before your school exams. If your score dips below 24, spend extra time on the 'Common Traps' section and drill medium-level questions (Q11–20) until you recognize patterns instinctively. For personalized feedback on your specific weaknesses—whether it's SI/CI logic, ratio simplification, or successive discount mechanics—consider a structured learning path at cbsetutor.ai with real tutors who can explain where your reasoning broke down. Start your free 3-day trial and get a diagnostic quiz score breakdown.