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Class 8 Maths Chapter 3 NCERT Solutions: A Story of Numbers

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Stepwise NCERT Solutions for Class 8 Maths Chapter 3 Exercises

Looking for reliable NCERT Solutions for Class 8 Maths Chapter 3 A Story of Numbers? Here you’ll find clear, stepwise explanations that make every exercise easy and exam-ready for students following the CBSE 2025–26 syllabus.


Our solutions are crafted to help you write better answers, use the right definitions, and apply formulas accurately. Get exercise-wise solutions that are structured just like your NCERT textbook, making it simple to follow and revise.


Download the free PDF for offline practice anytime! With these stepwise answers, you’ll be ready to tackle each question confidently and improve your score in Class 8 Maths Chapter 3.


Stepwise NCERT Solutions for Class 8 Maths Chapter 3 Exercises

1. Answer the following questions in about 30 words.


1. Who were the Marathas? How did they emerge as a leading power in India before the arrival of the British?


Answer: The Marathas were natives of the Deccan plateau, mainly in present-day Maharashtra, who spoke Marathi. Under Chhatrapati Shivaji Maharaj, they organized into a formidable political and military power. Through efficient administration, military innovation, and strategic leadership, they resisted Mughal dominance and expanded across India until the British gained ascendancy.


2. What were the main features of Maratha governance?


Answer: Maratha governance under Shivaji included a centralised administration, the aṣṭa pradhāna manḍala (council of eight ministers), revenue reforms, salaries for officials, rotation of appointments, justice for commoners, efficient taxation (chauth and sardeshmukhi), military and naval strength, religious tolerance, and encouragement for trade and culture.


3. Briefly describe the impact the Maratha Empire left in Indian history.


Answer: The Maratha Empire shaped Indian history by ending Mughal dominance in much of India, establishing the largest Indian state before the British, reviving indigenous governance and cultural pride, inspiring figures of resistance, demonstrating successful use of forts and navies, and encouraging future Indian nationalism.


2. Answer the following questions in about 150 words.


1. Analyse how geography guided Maratha military strategy and state formation.


Answer: The Marathas made expert use of geography—the Sahyadri mountains and the Konkan coast—to shape their strategies. The rugged terrain allowed practice of guerrilla warfare and construction of impregnable forts like Raigad, Pratapgad, and Sindhudurg, offering both refuge and strongholds for counter-attacks. Coastal access enabled the formation of a navy, securing trade and defending against foreign naval threats. The strategic positioning of forts atop hills and near trade routes facilitated state consolidation and revenue collection, ensuring resilience against invaders. Thus, geography was central to the rise and survival of the Maratha state.


2. Compare Shivaji and later Marathas' treatment of religious places and people of different faiths, using chapter examples.


Answer: Shivaji was known for his religious tolerance—despite waging war, he spared religious sites, including during the sacking of Surat. Shivaji patronised Sanskrit and Marathi culture but respected all communities. Later Marathas maintained similar values, encouraging diversity in Thanjavur and supporting social reforms under figures like Ahilyabai Holkar, who rebuilt temples and supported people of various backgrounds. Although some campaigns led to devastation (as in Bengal), the overall policy discouraged religious persecution.


3. Why were forts so important to the Marathas? How did these help them survive larger enemies?


Answer: Forts were the backbone of Maratha defence, providing secure refuges, bases for guerrilla operations, and controlling vital routes. Their strategic construction atop mountains made them difficult to capture. Even with smaller numbers, the Marathas resisted large Mughal and later British armies for decades, as the forts allowed quick retreats, surprise attacks, and long sieges to exhaust enemies. This defensive network ensured the state's survival during prolonged invasion.


4. What is meant by: “The British took India from the Marathas more than from the Mughals”? Provide chapter evidence.


Answer: By the late 18th century, Marathas controlled extensive regions and Delhi itself, while Mughal power had declined. The British fought three wars against the Marathas (not the Mughals) to gain Indian territory, only succeeding after defeating Maratha armies and alliances. Thus, British dominance in India replaced the Marathas, not the Mughals, as shown by British campaigns and the end of Maratha power in 1818.


3. Match the following.


Questions Answer
1. Prime Minister in Shivaji’s court (C) Pradhān
2. Council of Eight Ministers (A) aṣṭa pradhāna manḍala
3. Maratha naval leader (D) Kanhoji Angre
4. Chauth (B) 25% tax for protection

4. Write a short biography on any one Maratha leader (Kanhoji Angre, Bajirao I, Mahadji Shinde, Ahilyabai Holkar, Tarabai) for younger students. Include a challenge they overcame.


Answer: Ahilyabai Holkar: Ahilyabai Holkar, ruler of Indore, became famous for her wisdom, kindness, and development work. She rebuilt great temples like Kashi Vishwanath and Somnath and cared for her people by building wells, roads, and schools. As a woman leader, she faced challenges after her husband's death, but she ruled with courage and justice, setting an example for all generations.


NCERT Solutions Class 8 Maths Chapter 3 A Story of Numbers 2025-26

Mastering Class 8 Maths Chapter 3 A Story of Numbers is essential for building a strong foundation in arithmetic and number patterns. Our step-by-step NCERT solutions for 2025-26 are designed to make concepts easy and exam-ready for every learner.


By practicing these NCERT Class 8 chapter-wise solutions, you can boost your problem-solving ability and tackle tricky questions with confidence. Focus on understanding place value, properties of numbers, and patterns for top performance in your assessments.


Consistent revision using chapter exercises helps in quick recall and effective learning. Remember to review solved examples and practice regularly to strengthen your basics and score maximum marks in your exams.


FAQs on Class 8 Maths Chapter 3 NCERT Solutions: A Story of Numbers

1. What are NCERT Solutions for Class 8 Maths Chapter 3: A Story of Numbers, and how do they help in CBSE 2025–26 exams?

NCERT Solutions for Class 8 Maths Chapter 3: A Story of Numbers provide detailed, stepwise answers for all textbook exercises, adhering strictly to the CBSE 2025–26 syllabus and marking scheme. Using these solutions builds a strong conceptual foundation, enhances exam writing skills, and maximizes your marks in school assessments and final exams by clarifying every step in problem-solving.

2. How should I write stepwise NCERT answers in Chapter 3 to score full marks in Class 8 Maths?

To score full marks using the NCERT Solutions for Class 8 Maths Chapter 3, always structure your answers stepwise as shown below:

  1. Read the question carefully and underline key terms.
  2. State any formulas or definitions used.
  3. Show all calculation steps clearly, without skipping any logical transitions.
  4. Box the final answer and write it neatly.
  5. Review your answer for accuracy and completeness before submission.

3. Which types of questions from Class 8 Maths Chapter 3 are most important for CBSE board exams?

In Class 8 Maths Chapter 3: A Story of Numbers, high-priority questions for exams typically include application-based questions, conceptual reasoning, short formula-based sums, and problems involving number properties. Focusing on these promotes better marks as they closely align with CBSE’s current exam trends and marking patterns.

4. Are diagrams or definitions mandatory in NCERT Solutions for Class 8 Maths Chapter 3 answers?

Including well-labelled diagrams and accurate definitions, where required, in your NCERT Solutions for Class 8 Maths Chapter 3 answers can substantially increase your marks. Some questions explicitly ask for diagrams, while others benefit from clear definitions—always refer to Vedantu's solutions for model answers and best practices.

5. How can I structure long answers in Class 8 Maths Chapter 3 for maximum CBSE marks?

Long answers in the NCERT Solutions for Class 8 Maths Chapter 3 should be presented as follows:

  • Start with a brief introduction or definition relevant to the topic.
  • Use bullets or short paragraphs for each logical point.
  • Include diagrams or examples if appropriate.
  • Finish with a concise summary or final statement boxed or underlined.
  • Maintain clear handwriting and neat formatting throughout.

6. Where can I download the free PDF of NCERT Solutions for Class 8 Maths Chapter 3 – A Story of Numbers?

You can download the free PDF of NCERT Solutions for Class 8 Maths Chapter 3 – A Story of Numbers exclusively from Vedantu. This PDF contains comprehensive, exercise-wise, stepwise solutions, making offline revision easy and effective for CBSE exams.

7. Do examiners award partial marks for correct steps in Class 8 Maths Chapter 3 even if the final answer is wrong?

Yes, CBSE examiners often award partial marks in Class 8 Maths Chapter 3 if you show the correct steps even when the final answer is incorrect. Following the stepwise approach outlined in Vedantu’s NCERT Solutions increases your chance of securing partial credit for method accuracy.

8. Are NCERT Solutions enough for Class 8 Maths Chapter 3 exam preparation, or should I use additional resources?

NCERT Solutions for Class 8 Maths Chapter 3 cover all essential concepts and question types required for CBSE 2025–26 exams. For thorough preparation, practice all solved and unsolved exercises first. After that, refer to Vedantu's revision notes or exemplar solutions for extra practice on tricky problems.

9. What are some common mistakes students make in Class 8 Maths Chapter 3 and how can they be avoided?

Avoiding frequent errors in NCERT Solutions for Class 8 Maths Chapter 3 is crucial for scoring well. Watch out for:

  • Missing key steps in calculations.
  • Ignoring units or mislabelling diagrams.
  • Using incorrect formulae or definitions.
  • Rushing through word problems without analyzing requirements.
  • Forgetting to revise answers for accuracy.

10. How can I revise Class 8 Maths Chapter 3 quickly using Vedantu’s NCERT Solutions for board exams?

For rapid revision of NCERT Solutions for Class 8 Maths Chapter 3, follow these steps:

  1. Read through solved examples and chapter summaries.
  2. Attempt back exercise questions without referring to solutions.
  3. Use Vedantu’s revision planner (1-day, 3-day, 7-day) with flash notes for key concepts.
  4. Review common mistakes and marking scheme insights.

11. How do references to textbook page numbers assist in revising NCERT Solutions for Class 8 Maths Chapter 3?

Including textbook page numbers when using NCERT Solutions for Class 8 Maths Chapter 3 helps you cross-check with original explanations. This ensures you don’t miss context, allows for deeper understanding, and streamlines last-minute revision by quickly locating exact concepts and worked examples.

12. What is the best way to use chapterwise solutions for Class 8 Maths Chapter 3 from Vedantu for exam preparation?

For optimal exam preparation with NCERT Solutions for Class 8 Maths Chapter 3 from Vedantu, approach each exercise systematically. Begin by understanding the concept, solve practice questions independently, compare with Vedantu’s stepwise answers, and make a note of any gaps in your understanding for targeted revision. Regular practice fosters confidence and ensures exam readiness.