Chapter 11 Direct and Inverse Proportions Ex 11.2 NCERT Solutions for Class 8 Maths

Latest Updated : November 2023

If you are in search of NCERT solutions for Class 8 Maths Chapter 11 Direct and Inverse Proportions, then you are at the right place. When it comes to Mathematics, it is a subject that holds value for students across various academic streams, be it science, biology, or commerce and having a very good understanding of basic math concepts will help you in achieving your goal and make it much more easier.

Here we provide detailed NCERT solutions for Class 8 Maths of all the chapters, exercise wise with updated syllabus by NCERT. These NCERT solutions for Class 8 Maths have been carefully crafted to provide detailed explanations, ensuring that students can grasp the concepts effectively. We also provide extra practice questions for the same, so feel free to bookmark ncertforclass8.com to boost your preparation.

NCERT Solutions for Class 8 Maths Chapter 11 Direct and Inverse Proportions Ex 11.2

NCERT Solutions for Class 8 Maths Chapter 11 Direct and Inverse Proportions Ex 11.2

Class 8 Maths Chapter 11 Direct and Inverse Proportions Exercise 11.2

Exercise 11.2

1. 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) The number of workers and the time to complete the job is in inverse proportion because less workers will take more time to complete a job, and more workers will take less time to complete the same job.

(ii) Direct proportion.

(iii) Direct proportion because more are of cultivated land will yield more crops.

(iv) Inverse proportion because if time is less, speed is more.

(v) It is an inverse proportion. If the population of a country increases, the area of land per person decreases.

2. In a Television game show, the prize money of ` 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?

Number of winners124581020
Prize for each winner (in ₹)1,00,00050,000……………

Solution-

According to the question, the number of winners and prize money are in inverse proportion because winners are increasing, and prize money is decreasing.

\[When\ the\ number\ of\ winners\ is\ 4,\ each\ winner\ will\ get=\frac{100000}{4}=₹\ 25,000\]

\[When\ the\ number\ of\ winners\ is\ 5,\ each\ winner\ will\ get=\frac{100000}{5}=₹\ 20,000\]

\[When\ the\ number\ of\ winners\ is\ 8,\ each\ winner\ will\ get=\frac{100000}{8}=₹\ 12,500\]

\[When\ the\ number\ of\ winners\ is\ 10,\ each\ winner\ will\ get=\frac{100000}{10}=₹\ 10,500\]

\[When\ the\ number\ of\ winners\ is\ 20,\ each\ winner\ will\ get=\frac{100000}{20}=₹\ 5,000\]

3. 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-

Number of spokes4681012
Angle between a pair
of Consecutive spokes		90°60°………

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.

(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?

Solution-

According to the question, the number of spokes is increasing and the angle between a pair of consecutive spokes is decreasing.
So, it is an inverse proportion and the angle at the centre of a circle is 360°

\[When\ the\ number\ of\ spokes\ is\ 8,\ then\ the\ angle\ between\ a\ pair\ of\ con\sec utive\ spokes=\frac{360}{8}=\ 45°\]

\[When\ the\ number\ of\ spokes\ is\ 10,\ then\ the\ angle\ between\ a\ pair\ of\ con\sec utive\ spokes=\frac{360}{10}=\ 36°\]

\[When\ the\ number\ of\ spokes\ is\ 12,\ then\ the\ angle\ between\ a\ pair\ of\ con\sec utive\ spokes=\frac{360}{12}=\ 30°\]

Number of spokes4681012
Angle between a pair
of Consecutive spokes		90°60°45°36°30°

(i) Yes, the number of spokes and the angles formed between a pair of consecutive spokes is in inverse proportion.

(ii) When the number of spokes is 15, then the angle between a pair of consecutive spokes = 360/15= 24°

(iii) The number of spokes would be needed = 360/40 = 9

4. 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-

Each child gets = 5 sweets
24 children will get 24×5 = 120 sweets.
Also total number of sweets = 120
If the number of children is reduced by 4, then children left = 24-4 = 20

\[Now,\ each\ child\ will\ get\ sweets=\frac{120}{20}=6\ sweets\]

5. A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?

Solution-

Let the number of days be x.

Animals2030
Days6x

Total number of animals = 20+10 = 30

Here, the number of animals and the number of days are in inverse proportion.

\[∴\ \frac{20}{30}=\ \frac{x}{6}\]

\[⟹30\times\ x=20\times6\]

\[⟹x=\frac{20\times6}{30}=4\ days.\]

Hence, the food will last for four days.

6. A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?

Solution-

Let the time taken to complete the job be x.

Persons34
Days4x

Here, the number of persons and the number of days are in inverse proportion.

\[∴\ \frac{3}{4}=\frac{x}{4}\]

\[⟹4\times x=3\times4\]

\[⟹x=\frac{3\times4}{4}=\ 3\ days.\]

Hence, 4 persons will complete the job in 3 days.

7. A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?

Solution-

Let the number of boxes be x.

Number of boxes in each box1220
Boxes25x

Here, the number of bottles and the number of boxes are in inverse proportion.

\[∴\ \frac{12}{20}=\frac{x}{25}\]

\[⟹20\times x\ =\ 12\times25\]

\[⟹x=\frac{12\times25}{20}=15\ boxes\]

Hence, 15 boxes would be filled.

8. A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

Solution-

Let the number of machines required be x.

Days6354
Machines42x

Here, the number of machines and the number of days are in inverse proportion.

\[∴\ \frac{63}{54}=\frac{x}{42}\]

\[⟹54\times x=\ 63\times42\]

\[⟹\ x=\frac{63\times42}{54}=49\ machines\]

Hence, 49 machines would be required.

9. A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?

Solution-

Let the number of hours be x.

Speed (in Km/hour)6080
Time (in Hours)2x

Here, the speed of the car and time are in inverse proportion.

\[∴\ \frac{60}{80}=\frac{x}{2}\]

\[⟹\ 80\times x=60\times2\]

\[⟹\ x=\ \frac{60\times2}{80}=\ \frac{3}{2}=\ 1\ \frac{1}{2}\ hours\]

\[Hence\ the\ car\ will\ take\ \ 1\frac{1}{2}\ hours\ to\ reach\ the\ destination.\]

10. Two persons could fit new windows in a house in 3 days.

(i) One of the persons fell ill before the work started. How long would the job take now?
(ii) How many persons would be needed to fit the windows in one day?

Solution-

i) Let the number of days be x.

Persons21
Days3x

Here, the number of persons and the number of days are in inverse proportion.

\[∴\ \frac{2}{1}=\frac{x}{3}\]

\[⟹\ \ 1\times x=2\times3\]

\[⟹\ \ x=\frac{2\times3}{1}=6\ days\]

(ii) Let the number of persons be x.

Persons2x
Days31

Here, the number of persons and the number of days are in inverse proportion.

\[∴\ \ \frac{2}{x}=\frac{1}{3}\]

\[⟹\ 1\times x=2\times3\]

\[⟹\ x=\frac{2\times3}{1}=\ 6\ persons.\]

11. A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?

Solution-

Let the duration of each period be x.

Period89
Duration of period (in minutes)45x

Here, the number of periods and the duration of periods are in inverse proportion.

\[∴\ \ \frac{8}{9}=\frac{x}{45}\]

\[⟹\ 9\times x=8\times45\]

\[⟹\ x=\frac{8\times45}{9}=40\ \min utes\]

Hence, the duration of each period would be 40 minutes.

Using Class 8 NCERT solutions offers several key advantages for students:

  1. Accurate Answers: NCERT solutions for Class 8 Maths are prepared by expert educators and thoroughly reviewed to ensure quality and accurate answers.
  2. Aligned with Curriculum: NCERT Solutions for Class 8 Maths are specifically designed to go along with the CBSE curriculum, making them the ideal resource for students studying in CBSE affiliated schools.
  3. Crisp an Clear Explanation: The NCERT solutions for Class 8 Maths provide step by step explanations, making complex concepts easier to understand. This helps students to grasp the concepts easily and build a better foundation.
  4. Time-Saver: Instead of spending extra time searching for answers, students can quickly access these NCERT solutions for Class 8 Maths , saving time and allowing them to focus on other aspects of their studies.
  5. Extra Questions: NCERT Solutions for Class 8 Maths also has extra questions that offer additional opportunities for students to build better problem solving skills.
  6. Free Forever: We provide answers which will always be free to access and share.
  7. Self-Study Support: These are beneficial for students who prefer self study. They can independently work through the solutions and improve their understanding of the subject at their own pace.

Summary

On our platform ncertforclass8.com, you will get all the NCERT Solutions for Class 8 Maths expertly solved, ensuring utmost care and accuracy. The NCERT book for Class 8 Maths is strictly followed while creating the NCERT solutions for Class 8 Maths, adhering to the latest CBSE guidelines. We make sure to provide you quality content which will help you to understand the concepts in the best way possible. Also our solutions are completely free for you to access. You have the freedom to copy the NCERT Solutions for Class 8 Maths, download them and even create PDF’s, making it.

Leave a Comment

Scroll to Top