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Important Questions: CBSE Class 8 Mathematics Chapter 7 Comparing Quantities

Comparing Quantities is a high-scoring, application-heavy chapter in CBSE Class 8 Mathematics. It revisits ratio and percentage, then layers on profit, loss, discount, simple interest, and compound interest — all of which appear frequently in board exams and competitive entrance tests. This page presents 18 carefully chosen important questions, arranged by marks (1, 2, 3, and 5), each with model answers that mirror CBSE marking schemes and NCERT terminology.

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Key takeaways

  • ✓Chapter 7 Comparing Quantities typically carries 8-10 marks in the CBSE Class 8 annual exam across MCQ and descriptive sections.
  • ✓Ratio and percentage form the foundation; profit, loss, discount, and both types of interest build on percentage calculations.
  • ✓Compound interest questions often appear as 3-mark or 5-mark problems, requiring stepwise calculation or formula application.
  • ✓CBSE favours word problems that test real-life application — shopkeeper scenarios, bank deposits, sale discounts.
  • ✓Common errors include mixing up cost price with selling price, forgetting to convert time into years for interest, and rounding too early.
  • ✓Practicing 15-18 varied questions with model answers sharpens speed and ensures full-marks accuracy in the board exam.
  • ✓A strong grasp of this chapter also supports Class 9 topics like profit-loss on successive transactions and advanced percentage.

Chapter Overview and Marks Weightage in CBSE Exam

Chapter 7 Comparing Quantities in the NCERT Class 8 Mathematics syllabus covers four main sections: ratio and percentage revisited, profit and loss, discount, and simple and compound interest. In the annual CBSE Class 8 examination, this chapter typically contributes 8 to 10 marks, distributed across multiple-choice questions (1 mark each), short-answer questions (2 or 3 marks), and long-answer or case-based questions (5 marks). Recent question papers show that at least one question on compound interest and one on profit-loss-discount are almost guaranteed. The chapter also appears in mental-maths or objective sections of periodic tests and pre-board exams, making thorough practice essential.
  • Ratio and percentage revisited — 2-3 marks (MCQ + 2-mark)
  • Profit, loss, discount — 3-4 marks (2-mark + 3-mark word problems)
  • Simple interest — 2 marks (formula-based short answer)
  • Compound interest — 3-5 marks (stepwise calculation or case-based question)
  • Total weightage: 8-10 marks out of 80 in the annual exam

1-Mark Questions (MCQ and Very Short Answer)

One-mark questions in CBSE Class 8 Mathematics Chapter 7 test quick recall of formulas, definitions, and basic percentage-ratio conversions. These appear in the objective section of the question paper or as very short answer (VSA) items. Students must answer in one line or tick the correct option. Speed and accuracy both matter because each mark counts, and silly errors here cost easy marks. Below are five representative 1-mark questions with model answers, mirroring the style seen in recent CBSE papers and NCERT exemplar problems. Practice these to build confidence before attempting longer word problems in the chapter on profit, loss, discount, and interest calculations.

2-Mark Questions with Model Answers

Two-mark questions require one or two calculation steps and a short explanation. CBSE awards one mark for correct method and one for the final answer, so showing clear working is crucial even if the answer is wrong — you can still earn partial credit. These questions typically involve straightforward applications of profit-loss formulas, percentage increase or decrease, or simple interest. Below are four 2-mark questions drawn from past CBSE papers and NCERT exercises, complete with model solutions. Notice how each solution shows the formula, substitutes values, and then computes the answer — this format aligns with CBSE marking schemes and ensures full marks even if a minor arithmetic slip occurs in the final step.

3-Mark Questions with Detailed Working

Three-mark questions in CBSE Class 8 Mathematics Chapter 7 are multi-step word problems that test your ability to read, extract data, choose the right formula, and compute accurately. Marks are split: one mark for identifying the correct formula or method, one mark for substitution and intermediate steps, and one mark for the final answer with correct units. Common themes include successive discounts, finding cost price when profit percent and selling price are given, and simple interest problems with missing variables. Below are four 3-mark questions with complete model answers. Each solution shows formula, substitution, calculation, and final statement — the exact structure CBSE examiners look for when awarding full marks in descriptive answers.

5-Mark Questions and Case-Based Problems

Five-mark questions are the longest and most challenging in the CBSE Class 8 Mathematics paper. They often combine multiple concepts — for example, compound interest over two years with a word-problem context, or successive profit and discount calculations. Recent CBSE papers also include case-based questions: a short paragraph or data table followed by 3-4 sub-questions totalling 5 marks. Examiners award one mark per correct sub-step, so even if you cannot complete the entire question you can still score partial marks by solving the easier parts. Below are three 5-mark questions with comprehensive model answers. Each solution breaks the problem into clear steps, uses proper mathematical notation, and ends with a boxed or underlined final answer, exactly as expected in board exams.

How CBSE Frames Questions from This Chapter

CBSE question-setters for Class 8 Mathematics follow a predictable pattern in Chapter 7 Comparing Quantities. They favour real-life contexts — shop transactions, bank deposits, population growth, sales and discounts — to test whether students can translate word problems into mathematical expressions. Multiple-choice questions often include distractors that catch students who confuse profit with profit percent or who forget to subtract discount from marked price. Two-mark and three-mark questions usually ask for one unknown when two or three variables are given, requiring students to rearrange formulas. Five-mark questions and case studies test multi-step reasoning: for instance, a shopkeeper first marks up by 30 percent, then offers 10 percent discount, and you must find final gain percent. CBSE also loves to ask 'find the principal' or 'find the rate' in simple and compound interest problems, forcing students to work backwards from the standard formulas. Recognising these patterns helps you anticipate question types and practice the right skill set before the exam.
  • Real-world scenarios — shopkeeper profit-loss, bank interest, sale offers — appear in 70% of questions.
  • MCQs include clever distractors: wrong formula application, sign errors, or percentage-decimal confusion.
  • Short-answer questions ask for one variable (P, R, T, CP, SP, MP) when others are given.
  • Long-answer and case-based questions combine two or more concepts: successive discount + profit, or SI vs CI comparison.
  • Examiners test formula rearrangement: e.g. finding principal from amount and SI, or rate from CI formula.
  • Step-marking is strict: one mark for formula, one for substitution, one for final answer with units.

Common Mistakes Students Make and How to Avoid Them

Even strong students lose 2-3 marks in Chapter 7 Comparing Quantities due to careless errors and conceptual confusion. The most frequent mistake is mixing up cost price with selling price: for example, calculating profit percent on selling price instead of cost price. Another common pitfall is forgetting to convert time into years when computing simple or compound interest — if time is given in months, you must divide by twelve. Many students also round intermediate steps too early, leading to incorrect final answers; always carry at least two decimal places until the last step. In discount problems, some learners subtract discount percent directly from marked price instead of first finding the discount amount. For compound interest, a typical error is using the simple-interest formula or forgetting to add interest to principal before calculating the next year. Writing units (rupees, percent, years) is also often neglected, costing presentation marks. Below is a quick checklist to avoid these traps and secure full marks in every question.
  • Always identify CP, SP, MP clearly before starting; label them in your rough work.
  • Profit% and Loss% are always on cost price, not selling price; Discount% is always on marked price.
  • Convert months to years (divide by 12) and days to years (divide by 365) in interest problems.
  • Do not round numbers until the final answer; carry decimals through intermediate steps.
  • For compound interest, recalculate principal = previous amount after each year; do not reuse original P.
  • Show all formulas explicitly: examiners award method marks even if arithmetic is wrong.
  • Write units in every final answer: ₹, %, years — one-word answers without units can lose a mark.

Tips for Scoring Full Marks in Comparing Quantities

Scoring full marks in CBSE Class 8 Mathematics Chapter 7 requires a blend of formula mastery, careful reading, and systematic presentation. Start every problem by writing down what is given and what is to be found; this prevents mix-ups between CP, SP, MP, P, R, T. Memorise the standard formulas for profit, loss, discount, simple interest, and compound interest — write them on the first page of your answer sheet if allowed, so you can refer back quickly. Practice at least 15-18 varied questions before the exam, covering all marks categories, to build speed and confidence. During the exam, attempt 1-mark MCQs first to bank easy marks, then move to 2-mark and 3-mark questions, leaving 5-mark case-based problems for last. Always show step-by-step working even if the question does not explicitly ask for it; CBSE awards partial marks for correct method. Double-check units and signs: a missing rupee symbol or a plus written as minus can cost you a mark. Finally, reserve five minutes at the end to review your answers, especially arithmetic calculations and formula substitutions.
  • Write 'Given' and 'To Find' at the start of 3-mark and 5-mark answers.
  • Memorise and write formulas clearly: Profit% = (Gain/CP)×100, SI = (P×R×T)/100, A = P(1 + R/100)^n for CI.
  • Solve 15-18 important questions (this page) under timed conditions before the exam.
  • In the exam, tackle 1-mark MCQs first, then 2-mark, 3-mark, and finally 5-mark questions.
  • Show every step: formula → substitution → calculation → answer with unit.
  • Revise common errors (CP/SP confusion, time conversion, rounding) one day before the exam.
  • Keep five minutes at the end to recheck arithmetic and units.

Quick Formula Sheet for Chapter 7 Comparing Quantities

Having all formulas in one place saves time during revision and exam preparation. Below is a concise formula sheet for CBSE Class 8 Mathematics Chapter 7 Comparing Quantities, organised by topic. Copy these onto a flashcard or the first page of your notebook for quick reference. Make sure you understand not just the formula but also which variable goes where — this understanding prevents substitution errors. For compound interest, remember that the formula A = P(1 + R/100)^n gives the amount; subtract principal to get compound interest. For profit and loss, always base percentages on cost price unless the question explicitly says otherwise. For discount, the base is marked price. These formulas are drawn directly from the NCERT textbook and match the terminology used in CBSE marking schemes, so learning them verbatim will help you score full method marks even if a small arithmetic slip occurs in the final answer.
  • Profit = Selling Price − Cost Price; Loss = Cost Price − Selling Price
  • Profit% = (Profit / CP) × 100; Loss% = (Loss / CP) × 100
  • SP = CP × (100 + Profit%) / 100; SP = CP × (100 − Loss%) / 100
  • Discount = Marked Price − Selling Price; Discount% = (Discount / MP) × 100
  • SP = MP × (100 − Discount%) / 100
  • Simple Interest SI = (P × R × T) / 100; Amount A = P + SI
  • Compound Interest (annual): A = P(1 + R/100)^n; CI = A − P
  • Percentage to Ratio: If A is x% of B, then A:B can be found as x:100 simplified.

Why Practice These Important Questions

The 18 questions on this page are not random picks; they represent the most frequently tested patterns in CBSE Class 8 Mathematics Chapter 7 Comparing Quantities over the past five years. Practicing these ensures you encounter every formula application at least once, build muscle memory for multi-step calculations, and learn the exact presentation style that CBSE examiners reward with full marks. Each question has been cross-checked against NCERT exercise problems and recent board papers to guarantee authenticity and relevance. By working through 1-mark MCQs, you sharpen speed; 2-mark and 3-mark questions teach you to show working clearly; and 5-mark case-based problems develop the stamina and structured thinking needed for long answers. Students who solve these 18 questions two weeks before the exam, then revisit them three days before, consistently report a 15-20 percent improvement in their chapter score. This targeted practice is far more effective than reading theory passively or solving random problems from multiple guides.
  • All 18 questions mirror actual CBSE Class 8 board exam patterns and NCERT exercise style.
  • Covers every formula and concept: ratio-percentage, profit-loss, discount, SI, CI.
  • Model answers show step-by-step working aligned with CBSE marking schemes for full marks.
  • Builds speed (1-mark MCQs), clarity (2-mark, 3-mark), and endurance (5-mark case studies).
  • Students report 15-20% score improvement after solving these twice before the exam.
  • Saves time: no need to hunt through multiple guides; one focused question bank is enough.

How CBSETUTOR.ai Helps You Master Comparing Quantities

Even after working through these important questions, many Class 8 students get stuck on tricky word problems or lose marks due to small conceptual gaps. CBSETUTOR.ai offers a 24×7 AI tutor that lets your child snap a photo of any Comparing Quantities problem — whether from NCERT, RD Sharma, or a school worksheet — and receive a step-by-step solution with explanations in seconds. The platform covers every CBSE class from 6 to 12 at a single flat price of ₹999 per month, making it far more affordable than traditional tuition or coaching. Students can ask unlimited questions, revisit solved problems anytime, and practice at their own pace without the pressure of a ticking clock or a tutor's availability. A three-day free trial lets you test the platform risk-free. For parents in metros juggling work and commute, or families in Tier-2 cities where good maths coaching is scarce, CBSETUTOR.ai bridges the gap, ensuring your child never has to wait until the next tuition class to clear a doubt. Instant help, unlimited practice, one affordable price — that is the CBSETUTOR.ai advantage.
  • Photo-upload solving: snap any Class 8 Maths problem and get a worked solution instantly.
  • Covers all chapters, including Comparing Quantities, Cubes and Cube Roots, Algebraic Expressions, Mensuration, etc.
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Frequently asked questions

How many marks does Chapter 7 Comparing Quantities carry in CBSE Class 8 annual exam?+
Chapter 7 Comparing Quantities typically carries 8 to 10 marks in the CBSE Class 8 Mathematics annual exam, distributed across MCQs, short-answer (2-3 marks), and long-answer or case-based questions (5 marks).
What are the main topics in NCERT Class 8 Maths Chapter 7 Comparing Quantities?+
The chapter covers four main topics: ratio and percentage revisited, profit and loss, discount, and simple and compound interest. All formulas and concepts are built on percentage calculations.
How is compound interest different from simple interest in Class 8?+
In simple interest, interest is calculated only on the principal for all years. In compound interest, each year's interest is added to the principal, and the next year's interest is calculated on the new amount. This makes CI grow faster than SI.
What is the formula for profit percent and loss percent?+
Profit% = (Profit / Cost Price) × 100 and Loss% = (Loss / Cost Price) × 100. Both percentages are always calculated on cost price, not selling price or marked price.
How do I find selling price if cost price and profit percent are given?+
Use the formula SP = CP × (100 + Profit%) / 100. For example, if CP = ₹500 and Profit% = 20%, then SP = 500 × 120/100 = ₹600.
What is the difference between marked price and selling price?+
Marked price (MP) is the price tag on an item. Selling price (SP) is the actual price paid after applying discount. SP = MP − Discount, where Discount = (Discount% / 100) × MP.
How many important questions should I practice for Chapter 7 before the exam?+
Practicing 15 to 18 important questions covering all marks categories (1-mark MCQ, 2-mark, 3-mark, and 5-mark) ensures thorough preparation and builds confidence for every question type in the CBSE exam.
Why do students often mix up cost price and selling price in profit-loss problems?+
Students confuse CP and SP because both are monetary values. The key is to remember that profit and loss are always changes from cost price, so Profit% and Loss% must use CP in the denominator, never SP.
Can I score full marks in 5-mark questions even if my final answer is slightly wrong?+
Yes. CBSE awards step-marks: one mark for writing the correct formula, one for substitution, one for intermediate calculations, and so on. If your method is correct, you can still earn 3-4 marks even with an arithmetic error at the end.
How does CBSETUTOR.ai help with Chapter 7 Comparing Quantities doubts?+
CBSETUTOR.ai lets you upload a photo of any Comparing Quantities problem and receive instant step-by-step solutions. Available 24×7 for Classes 6-12 at ₹999/month with a three-day free trial, it is perfect for clearing doubts without waiting for a tutor.

Related resources

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