Class 9 Mathematics Chapter 10: Ratios, Proportions and Percentages — Previous Year Questions with Solutions

When you study theory from your textbook, your brain learns concepts in isolation. When you solve a PYQ, your brain learns *how to apply* those concepts under time pressure, with unfamiliar numbers and wording. Past papers reveal three critical truths: (1) *What examiners actually test*—not every formula or sub-topic gets equal weight; Chapter 10 heavily favours percentage-increase problems and profit-loss scenarios over pure ratio definitions. (2) *Common error patterns*—examiners design wrong options to catch students who miscalculate percentage changes or confuse profit margin with profit percentage. (3) *Time management*—a 1-mark ratio simplification should take 30 seconds; a 5-mark simple interest question with multiple steps should take 4 minutes. Theory doesn't teach timing; PYQs do. Research shows students who solve 10–15 past papers before exams score 15–20% higher than peers who only study theory. Your confidence grows measurably when you recognize a question type you've solved before.

**Question 1:** Simplify the ratio 48:64. *Answer:* 3:4 *Solution:* Find GCD(48, 64) = 16. Divide both: 48÷16 = 3, 64÷16 = 4. **Question 2:** If a:b = 2:3 and b:c = 4:5, find a:c. *Answer:* 8:15 *Solution:* a:b:c requires same b value. Rewrite a:b = 8:12 (multiply by 4) and b:c = 12:15 (multiply by 3). So a:b:c = 8:12:15, thus a:c = 8:15. **Question 3:** Express 35% as a ratio in simplest form. *Answer:* 7:20 *Solution:* 35% = 35/100 = 7/20. Ratio form: 7:20. **Question 4:** If 5 notebooks cost ₹180, find cost of 12 notebooks. *Answer:* ₹432 *Solution:* Cost of 1 notebook = 180÷5 = ₹36. Cost of 12 = 36×12 = ₹432. **Question 5:** What is 18% of 250? *Answer:* 45 *Solution:* 18% × 250 = (18/100) × 250 = 0.18 × 250 = 45. *Examiner Tip:* 1-mark questions test speed and accuracy. Ratio simplification uses GCD; percentage calculations require fraction conversion. Practise mental maths for quick answers.

**Question 1:** A shopkeeper buys a book for ₹120 and sells it for ₹150. Find profit percentage. *Solution:* Profit = SP − CP = 150 − 120 = ₹30 Profit % = (Profit/CP) × 100 = (30/120) × 100 = 25% *Answer:* 25% **Question 2:** Divide ₹500 in the ratio 3:7 between A and B. *Solution:* Total parts = 3 + 7 = 10 A's share = (3/10) × 500 = ₹150 B's share = (7/10) × 500 = ₹350 *Answer:* A gets ₹150, B gets ₹350 **Question 3:** The price of petrol increased by 20%. If the original price was ₹80/litre, find the new price. *Solution:* Increase = 20% of 80 = (20/100) × 80 = ₹16 New price = 80 + 16 = ₹96/litre *Answer:* ₹96/litre **Question 4:** Find simple interest on ₹2000 at 8% per annum for 3 years. *Solution:* SI = (P × R × T)/100 = (2000 × 8 × 3)/100 = 48000/100 = ₹480 Amount = P + SI = 2000 + 480 = ₹2480 *Answer:* SI = ₹480, Amount = ₹2480 **Question 5:** If the ratio of boys to girls in a class is 5:6 and there are 55 boys, find total students. *Solution:* Boys:Girls = 5:6. Boys = 5 units = 55, so 1 unit = 11 Girls = 6 units = 6 × 11 = 66 Total = 55 + 66 = 121 *Answer:* 121 students *Examiner Tip:* 3-mark questions combine two concepts. Always show working: identify formula, substitute values, simplify. Partial marks awarded for correct method even if final answer is wrong.

**Question 1:** A shopkeeper sells a chair for ₹1200 at a loss of 10%. Find cost price. If he wishes to make 15% profit, at what price should he sell it? *Full Solution:* Let CP = x Loss = 10%, so SP = 90% of CP 1200 = (90/100) × x 1200 = 0.9x x = 1200/0.9 = ₹1333.33 For 15% profit: SP = CP + 15% of CP = 115% of CP SP = (115/100) × 1333.33 = 1.15 × 1333.33 = ₹1533.33 *Answer:* Cost Price = ₹1333.33; Selling Price for 15% profit = ₹1533.33 **Question 2:** A sum of ₹5000 is divided among three people in the ratio 1:2:3. Find each person's share. If each share is deposited in a bank at 10% simple interest per annum for 2 years, find total amount after 2 years. *Full Solution:* Total ratio parts = 1 + 2 + 3 = 6 Shares: First = (1/6) × 5000 = ₹833.33, Second = (2/6) × 5000 = ₹1666.67, Third = (3/6) × 5000 = ₹2500 For each share, SI = (P × R × T)/100 First: SI = (833.33 × 10 × 2)/100 = ₹166.67, Amount = 833.33 + 166.67 = ₹1000 Second: SI = (1666.67 × 10 × 2)/100 = ₹333.33, Amount = 1666.67 + 333.33 = ₹2000 Third: SI = (2500 × 10 × 2)/100 = ₹500, Amount = 2500 + 500 = ₹3000 Total Amount = 1000 + 2000 + 3000 = ₹6000 *Answer:* Total amount after 2 years = ₹6000 **Question 3:** A merchant purchases goods for ₹8000 and marks up the price by 40%. He offers a discount of 15% on the marked price. Calculate selling price, profit, and profit percentage. *Full Solution:* Cost Price = ₹8000 Marked Price = CP + 40% of CP = (140/100) × 8000 = ₹11200 Discount = 15% of MP = (15/100) × 11200 = ₹1680 Selling Price = MP − Discount = 11200 − 1680 = ₹9520 Profit = SP − CP = 9520 − 8000 = ₹1520 Profit % = (Profit/CP) × 100 = (1520/8000) × 100 = 19% *Answer:* Selling Price = ₹9520, Profit = ₹1520, Profit % = 19% *Examiner Tip:* 5-mark questions test end-to-end problem-solving. Structure your answer: state given data, identify formula, show all intermediate steps, box your final answer. Marks are awarded for method, not just the final number. A calculation error loses 1–2 marks, but correct method keeps you at 3–4 marks.

The 2024–25 rationalized syllabus emphasises real-world application over abstract theory. Three observable shifts in recent papers: (1) *Higher emphasis on word problems*—pure ratio/proportion questions are rare; instead, examiners embed ratios inside profit-loss or percentage scenarios. Example: 'A profit of ₹400 is shared between partners in ratio 2:3. Find each partner's profit and profit percentage.' This tests ratio *and* profit simultaneously. (2) *Multi-step reasoning*—5-mark questions now often combine simple interest with percentage changes or ratio division. Students must identify which concept to apply at each step. (3) *Real financial contexts*—examples now reference GST, bank interest, discounts, and business scenarios rather than abstract 'A and B' problems. This aligns with the NEP 2020 focus on practical life skills. Percentage questions now explicitly ask for increase/decrease interpretation, not just calculation. Students scoring high recognize these patterns early and allocate study time accordingly—70% of your Chapter 10 revision should target profit-loss and percentage applications, 20% to simple interest chains, 10% to pure ratios.

**During Exam (2.5 hours total; Chapter 10 typically 12–15 marks out of 80):** **Minute 0–5:** Read all questions. Identify question type: ratio simplification (fastest), percentage (medium), profit-loss (slowest). Mentally map out: 1-mark questions = 2–3 mins total, 3-mark questions = 6–9 mins total, 5-mark questions = 12–15 mins total. **Minute 5–20:** Solve all 1-mark ratio and percentage questions first. These are confidence-builders and low-risk. Use scratch space for GCD calculations. **Minute 20–50:** Tackle 3-mark profit-loss and simple interest problems. Show three lines minimum: (1) identify formula, (2) substitute values, (3) simplify. Even if final answer is wrong, examiners award 2/3 marks for correct method. **Minute 50–65:** Attempt 5-mark questions. Read twice. For multi-step problems: divide into sub-questions on paper. Example: "A shopkeeper... marks... discounts... find profit%" → break into (i) find marked price, (ii) find selling price, (iii) find profit %, (iv) interpret. This segmentation prevents panic and improves accuracy. **Minute 65–75:** Review answers. Recalculate percentage and SI formulas using a different method to verify. Check: Did I use rate as percentage or decimal? Did I miss 'total' vs 'per person'? **When Stuck:** Move on. A 3-mark question left blank = 0 marks; three 1-mark questions = 3 marks. Time spent on one hard question loses easier marks elsewhere.

This guide covers 13 representative PYQs; authentic CBSE papers contain variation. To deepen mastery: (1) Solve questions from official CBSE sample papers (2024–25 onwards), available free at cbse.gov.in. (2) Time yourself: 1-mark in 45–60 seconds, 3-mark in 3 minutes, 5-mark in 5 minutes. (3) Identify *your* error pattern—do you misread 'profit on cost' vs 'profit on selling price'? Do you convert percentages to decimals correctly? Targeted revision fixes these faster than re-solving every question. (4) Cross-check: Use the inverse formula. If profit % = 25%, verify by calculating back to cost price. Many students catch errors this way. CBSE Chapter 10 success hinges on repetition with feedback. Past papers provide authentic feedback; your textbook provides theory. Combine both systematically for 90+ scores.