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CBSE Class 8 Mathematics Chapter 7 Comparing Quantities Worksheet with Answers

Comparing Quantities is a cornerstone chapter in CBSE Class 8 Mathematics, bridging arithmetic with real-life financial literacy. This printable worksheet provides rigorous practice on ratio and percentage, profit-loss-discount, and both simple and compound interest. Designed for 90 minutes of focused work, it progresses from objective questions to higher-order thinking problems, ensuring conceptual clarity and application skills. Use this worksheet for self-assessment, classroom tests, or targeted revision before exams.

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Key takeaways

✓Complete printable worksheet covering all topics: ratio-percentage, profit-loss-discount, simple and compound interest as per NCERT Class 8 Mathematics Chapter 7.
✓Structured into five progressive sections from MCQs to HOTS questions, with a real-world case-study to develop application skills.
✓90-minute timed practice at medium-to-advanced difficulty prepares students for board exams and school assessments effectively.
✓Every question includes detailed solutions in the answer key section, enabling independent learning and error correction.
✓Aligns perfectly with CBSE Class 8 Mathematics syllabus and 2025 board exam pattern for Comparing Quantities.
✓Suitable for classroom tests, homework assignments, and self-study revision before half-yearly or final examinations.

Quick Chapter Recap: Comparing Quantities

Chapter 7 of NCERT Class 8 Mathematics revisits ratio and percentage with deeper applications, introducing students to commercial mathematics concepts like profit, loss, discount, and both simple and compound interest. Ratios express relative sizes of two quantities; percentages convert these into per-hundred notation for easier comparison. Profit and loss calculations involve cost price (CP), selling price (SP), overhead expenses, and discount on marked price. Simple Interest (SI) is calculated on the principal for the entire time period, while Compound Interest (CI) accumulates interest on both principal and previously earned interest, compounded annually, half-yearly, or quarterly. Mastering these concepts builds financial literacy essential for informed decision-making in everyday life and higher mathematics.

Percentage = (Part/Whole) × 100; used extensively in profit-loss and interest calculations.
Profit = SP – CP; Loss = CP – SP; Profit% or Loss% always on Cost Price.
Discount is a reduction on Marked Price (MP); SP = MP – Discount.
Simple Interest = (P × R × T)/100 where P=Principal, R=Rate per annum, T=Time in years.
Compound Interest: Amount = P(1 + R/100)^n; CI = Amount – P.
For rates compounded half-yearly, use R/2 and 2T; quarterly, use R/4 and 4T.

Worksheet Information: Difficulty Level and Suggested Time

This worksheet is pitched at medium to advanced difficulty, suitable for students who have completed initial NCERT Class 8 Mathematics Chapter 7 exercises and are preparing for school exams or CBSE board assessments. The questions demand conceptual understanding, multi-step problem-solving, and real-world application skills. Allocate 90 minutes to complete all sections under timed conditions to simulate exam pressure. Students scoring above 80% demonstrate strong command; those scoring 60-80% should revisit weaker topics; below 60% indicates the need for conceptual revision using NCERT textbook and additional Class 8 Mathematics solutions. Attempt the worksheet without a calculator to build mental math agility. Use the detailed answer key only after completing all sections honestly.

Difficulty Level: Medium to Advanced
Suggested Time: 90 minutes (strict timing recommended)
Total Marks: 50 (MCQs: 6 marks; Fill-in-blanks: 5 marks; Match/True-False: 4 marks; Short answer: 15 marks; Long answer: 15 marks; Case study: 5 marks)
No calculators; show all working in the margin
Self-assess using the answer key only after attempting all questions

Section A: Multiple Choice Questions (6 Marks)

Each MCQ carries 1 mark. Choose the correct option and write the letter in your answer sheet. These questions test your quick recall and application of formulas for ratio, percentage, profit-loss, discount, and interest calculations. Read each question carefully, eliminate obviously wrong options, and compute where necessary. MCQs often feature common student errors as distractors, so double-check your arithmetic. This section should take approximately 12 minutes. Write neatly and ensure you mark only one option per question. In board exams, erasing or overwriting can lead to confusion during evaluation.

Section B: Fill in the Blanks (5 Marks)

Each blank carries 1 mark. Write precise numerical answers or brief phrases. Fill-in-the-blank questions demand exact recall of definitions, formulas, and standard results from NCERT Class 8 Mathematics Chapter 7. Avoid vague or incomplete answers; units like %, ₹, or years must be included where appropriate. This section should take around 10 minutes. These questions often test your grasp of terminology and formula structure, so revise your Class 8 Mathematics notes before attempting. If stuck, move on and return after completing other sections; sometimes later questions trigger memory.

Section C: Match the Following / True or False (4 Marks)

This section includes 4 statements; write True or False for each. Each correct response earns 1 mark. These statements assess your conceptual clarity on common misconceptions and fine distinctions in ratio, percentage, profit-loss, discount, and interest. Read each statement twice before answering. In board and school exams, True/False questions often penalise hasty reading. Allocate 8 minutes to this section. If a statement includes the words 'always', 'never', or 'only', scrutinise whether exceptions exist. Cross-check your answers against NCERT Class 8 Mathematics definitions and worked examples.

Section D: Short Answer Questions (15 Marks)

Each short-answer question carries 3 marks. Show all steps clearly; partial credit is awarded for correct method even if the final answer is wrong. These questions require two to three calculation steps and application of one or two formulas. Time allocation: 25 minutes. Write units and label intermediate results (CP, SP, SI, CI, etc.) to avoid confusion. If a question has two parts, answer both; marks are often split 1.5 + 1.5 or 2 + 1. Short-answer questions in CBSE Class 8 Mathematics exams test your procedural fluency and ability to communicate mathematical reasoning clearly. Revise standard problem types from NCERT exercises 7.1, 7.2, and 7.3 before attempting.

Section E: Long Answer / HOTS Questions (15 Marks)

Each long-answer question carries 5 marks and demands multi-step reasoning, synthesis of concepts, or higher-order thinking. Time allocation: 25 minutes. These questions mirror board exam patterns where students must integrate ratio-percentage with profit-loss or compare simple and compound interest. Write every step with justification; examiners award marks for logical progression even if the final answer has a minor arithmetic slip. HOTS (Higher Order Thinking Skills) questions test whether you can apply Comparing Quantities concepts to unfamiliar or real-world scenarios. Practise similar problems from Class 8 Mathematics solutions and previous years' CBSE question papers. Clarity in presentation often earns bonus impression marks.

Section F: Case Study Based Question (5 Marks)

Read the case study carefully and answer the sub-questions that follow. Case-study questions have become a staple in CBSE board exams from 2020 onwards, testing your ability to extract mathematical information from real-life scenarios. This question carries 5 marks split across 2-3 sub-parts. Allocate 10 minutes. Underline key numerical data in the passage and identify which formula or concept applies to each sub-question. Even if you find one part difficult, attempt the others; marks are independent. Case studies integrate Comparing Quantities with data interpretation, reinforcing financial literacy and practical application skills essential for informed citizenship.

Answer Key with Detailed Solutions

Below are the complete solutions for every question in the worksheet. Review your work honestly before checking answers. For incorrect responses, identify whether the error was conceptual (formula misapplication), procedural (arithmetic mistake), or reading (misunderstood question). Write notes in the margin for topics requiring revision. If you score below 60%, revisit NCERT Class 8 Mathematics Chapter 7 text, solve all NCERT examples again, and consult Class 8 Mathematics notes or a tutor. CBSETUTOR.ai offers 24×7 doubt-solving with photo upload, covering all chapters at ₹999/month flat for Classes 6-12, with a 3-day free trial—perfect for clearing Comparing Quantities confusion instantly. Use this answer key as a learning tool, not just a marking scheme. Understanding why an answer is correct or wrong is the key to mastering Comparing Quantities.

How to Use This Worksheet Effectively for Exam Preparation

To maximise learning, print this worksheet and attempt it under timed, exam-like conditions without referring to notes or NCERT Class 8 Mathematics textbook. Use a stopwatch and allocate section-wise time as suggested. After completion, self-assess using the answer key and calculate your score out of 50. Identify weak areas—if you struggled with compound interest, revisit NCERT Exercise 7.3 and solve additional problems. Reattempt incorrect questions after a day or two to check retention. For peer learning, exchange worksheets with classmates and discuss solutions. Teachers can use this worksheet for periodic assessments or homework assignments. Parents should encourage children to explain their solutions aloud; verbalising mathematical reasoning deepens understanding. Regular practice with such structured worksheets builds confidence and speed, both critical for scoring well in CBSE board exams.

Print the worksheet and attempt in one sitting under timed conditions
Self-assess using the answer key; calculate percentage score
Revisit NCERT chapters for topics where you scored below 70%
Reattempt incorrect questions after 2 days to test retention
Discuss solutions with peers or teachers for collaborative learning
Use as a diagnostic tool before school exams or term tests

Common Mistakes Students Make in Comparing Quantities

Many students confuse profit percentage base: profit% is always on cost price, never on selling price. Another frequent error is adding successive discounts arithmetically; two discounts of 20% and 10% do NOT equal 30%—you must calculate each on the reduced price. In compound interest, students forget to adjust rate and time for half-yearly or quarterly compounding. For half-yearly, use R/2 and 2T; for quarterly, R/4 and 4T. Mixing up marked price and selling price in discount problems is common; discount is always on marked price. In ratio problems, students sometimes add or subtract ratios directly without finding the common multiplier. When solving interest problems, ensure you distinguish between simple and compound interest formulas. Finally, many forget to write units (%, ₹, years) in answers, leading to mark deductions in board exams. Avoid these pitfalls by practising carefully and reviewing NCERT Class 8 Mathematics worked examples.

Calculating profit% on SP instead of CP
Adding successive discounts instead of applying step-by-step
Forgetting to halve rate and double time for half-yearly CI
Confusing marked price with selling price in discount sums
Direct addition/subtraction of ratios without finding the multiplier
Omitting units (%, ₹, years) in final answers

Why Choose CBSETUTOR.ai for Comparing Quantities Doubts

Comparing Quantities can be tricky with its mix of percentages, multi-step profit-loss problems, and compound interest calculations. CBSETUTOR.ai provides 24×7 AI-powered tutoring, letting your child snap a photo of any worksheet problem and receive instant step-by-step solutions. Whether it is a confusing successive discount question at 10 PM or a compound interest problem during weekend revision, help is always available. The platform covers every NCERT Class 8 Mathematics chapter, aligning perfectly with CBSE syllabus and latest board exam patterns. At a flat ₹999 per month for all subjects across Classes 6-12, it is far more affordable than traditional tuition or coaching centres. Parents appreciate the transparent pricing—one price, unlimited doubts. A 3-day free trial lets students explore the platform risk-free. Thousands of CBSE families trust CBSETUTOR.ai to fill gaps, clarify concepts, and build exam confidence without the stress of commute or rigid class timings.

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Frequently asked questions

What topics are covered in CBSE Class 8 Mathematics Chapter 7 Comparing Quantities?+

Chapter 7 covers ratio and percentage revisited, profit and loss calculations including cost price and selling price, discount on marked price, and both simple and compound interest. These topics build financial literacy and appear regularly in board exams.

How much time should I spend on this Comparing Quantities worksheet?+

Allocate 90 minutes under timed conditions. Section-wise: MCQs 12 min, Fill-in-blanks 10 min, True/False 8 min, Short answer 25 min, Long answer 25 min, Case study 10 min. This simulates real exam pressure and builds speed.

What is the difference between simple interest and compound interest?+

Simple Interest is calculated on the principal for the entire period. Compound Interest accumulates interest on principal plus previously earned interest. CI is always greater than SI for time beyond one year at the same rate. Formula: SI = (P×R×T)/100; CI = P(1+R/100)^n – P.

How do I calculate profit percentage and loss percentage?+

Profit% = [(SP – CP)/CP] × 100 if SP > CP. Loss% = [(CP – SP)/CP] × 100 if CP > SP. Always calculate percentage on cost price, not selling price. Include overhead expenses in total CP if mentioned.

What is the correct method to calculate successive discounts?+

Apply each discount step-by-step on the reduced price, never add them directly. For example, 20% then 10%: first discount leaves 80% of MP, second discount is 10% on that 80%, total effective discount is 28%, not 30%.

How is compound interest calculated for half-yearly compounding?+

For half-yearly compounding, use rate R/2 and time 2T. Formula becomes A = P(1 + R/200)^(2T). For quarterly, use R/4 and 4T. This accounts for interest being added more frequently, increasing total interest earned.

Why is this worksheet useful for CBSE board exam preparation?+

This worksheet mirrors the CBSE exam pattern with MCQs, short and long answers, HOTS, and case-study questions. It covers all NCERT Class 8 Mathematics Chapter 7 topics, builds speed and accuracy, and includes detailed solutions for self-assessment and concept reinforcement.

What should I do if I score below 60% on this worksheet?+

Revisit NCERT Class 8 Mathematics Chapter 7 text and solve all in-text and exercise problems again. Focus on weak areas identified in the answer key. Consider using CBSETUTOR.ai for personalised doubt-solving and additional practice to strengthen concepts before reattempting the worksheet.

Can I use a calculator while solving this worksheet?+

No, avoid calculators to build mental math skills and calculation speed essential for board exams. CBSE permits basic calculations without electronic aids. Practice arithmetic carefully to reduce silly errors and improve confidence in numerical problem-solving.

How does CBSETUTOR.ai help with Comparing Quantities doubts?+

CBSETUTOR.ai offers 24×7 AI tutoring where students upload photos of problems and receive instant step-by-step solutions. It covers all NCERT chapters, aligns with CBSE syllabus, costs ₹999/month flat for Classes 6-12, and offers a 3-day free trial for risk-free exploration.

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