13. Direct and Inverse Proportions

NCERT Solutions for Class 8 – Complete Chapter-wise Study Material

13. Direct and Inverse Proportions is one of the most important chapters in the Class 8 Mathematics English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.

The 13. Direct and Inverse Proportions - Class 8 Mathematics English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.

One of the biggest advantages of studying 13. Direct and Inverse Proportions is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.

Our Class 8 Mathematics NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.

Students preparing for school assessments should carefully study 13. Direct and Inverse Proportions because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.

At ATP Education, we continuously update our Class 8 Mathematics English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying 13. Direct and Inverse Proportions thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.

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13. Direct and Inverse Proportions - Class 8 Mathematics English NCERT Solutions

Class 8 Mathematics English Updated : 06 March 2026

Exercise 13.1

Q1. Following are the car parking charges near a railway station upto

4 hours Rs 60

8 hours Rs 100

12 hours Rs 140

24 hours Rs 180

Check if the parking charges are in direct proportion to the parking time.

Solution :

Q2. A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.

Q3. In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Solution:

Q4. A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Solution:

Q5. A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Q6. In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?

Therefore the length of model ship is 21 cm.

Q7. Suppose 2 kg of sugar contains 9 × 10⁶ crystals.

How many sugar crystals are there in

(i) 5 kg of sugar?

(ii) 1.2 kg of sugar?

Solution:

Q8. Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Q9. A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time

(i) The length of the shadow cast by another pole 10 m 50 cm high

(ii) The height of a pole which casts a shadow 5m long.

Solution:

Q10. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

Solution:

13. Direct and Inverse Proportions

Class 8 Mathematics English Updated : 06 March 2026

Exercise 13.2

Q1. Which of the following are in inverse proportion?

(i) The number of workers on a job and the time to complete the job.

(ii) The time taken for a journey and the distance travelled in a uniform speed.

(iii) Area of cultivated land and the crop harvested.

(iv) The time taken for a fixed journey and the speed of the vehicle.

(v) The population of a country and the area of land per person.

Solution:

(i) Numbers of workers on a job and time always be in inverse proportion because when we increase in workers time reduces and when we reduce in workers time it take more time.

(ii) The time taken and distance are in direct proportion because if we increase in time it covers more distance. Hence both quantities increase together.

(iii) As area will be cultivated as more crops will be harvested. So these are direct proportion.

(iv) Time and speed always be in inverse proportion. As we increase the time we have to reduce the speed to cover a fixed distance. Similarly we see that if we increase the speed time reduces automatically.

(v) If population is increased area land will be short to live. Therefore these both quantity are in inverse proportion.

Q2. In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

Solution: Prize will be distributed to winner in inverse proportion.

As both quantities are in inverse proportion.

Suppose the table has …

Q3. Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

Solution:

The relation between spokes and angle between consecutive spokes are in inverse proportion.

Therefore, X₁Y₁ = X₂Y₂

Q4. If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?

Solution:

According to question we have the table like this

13. Direct and Inverse Proportions

Class 8 Mathematics English Updated : 06 March 2026

raराम एक अच्चा लड़का है |

वह इसी गाँव में रहता है |

मैं एक डॉक्टर हूँ |

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13. Direct and Inverse Proportions - Class 8 Mathematics English NCERT Solutions

NCERT Solutions for Class 8 – Complete Chapter-wise Study Material

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13. Direct and Inverse Proportions - Class 8 Mathematics English NCERT Solutions

13. Direct and Inverse Proportions

13. Direct and Inverse Proportions

Exercise 13.2

13. Direct and Inverse Proportions

NCERT Book Solutions

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Chapter 1. Rational Numbers Solutions

Chapter 2. Linear Equations in One Variable Solutions

Chapter 3. Understanding Quadrilaterals Solutions

Chapter 4. Practical Geometry Solutions

Chapter 5. Data Handling Solutions

Chapter 6. Squares and Square Roots Solutions

Chapter 7. Cubes and Cube Roots Solutions

Chapter 8. Comparing Quantities Solutions

Chapter 9. Algebraic Expressions and Identities Solutions

Chapter 10. Visualising Solid Shapes Solutions

Chapter 11. Mensuration Solutions

Chapter 12. Exponents and Powers Solutions

Chapter 13. Direct and Inverse Proportions Solutions

Chapter 14. Factorisation Solutions

Chapter 15. Introduction to Graphs Solutions

Chapter 16. Playing with Numbers Solutions

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