Direct and Inverse proportion chapter is part of ratio and proportion topic, where we have relation between two entities. Direct proportion relates to direct ratio, for example with same speed, distance travel will increase by time. Indirect proportion happen when with increase of value of one entity, second value decreases. For example, given a same work, if we have more workers, then time taken to complete the work will decrease.

Direct and inverse proportion chapter is covered best in the NCERT books for class 8 maths book, which offers various examples and exercise to understand different concepts.

NCERT books are recommended course text books for students following Indian curriculum. They have been followed by CBSE and all other major school boards in India and abroad. Almost all of the public and private schools recommend this books to their students.

In this article, we have discussed about the Class 8 maths NCERT exercises for direct and inverse proportion. We have provided detailed video solutions of NCERT problems for Class 8. Students can look into solved NCERT exercises for class 8 mathematics.

Though direct and inverse proportion chapter looks easy, but many students face difficulties in understanding questions related to indirect proportion. These solved NCERT problems for class 8 will help in clearing the concepts of direct and inverse proportion chapter, and also make student understand in how to avoid common mistakes in direct and inverse proportion chapter.

## Class 8 math ncert solution direct and indirect proportion chapter

**Exercise 13.1 solutions**

Q1 – Following are the car parking charges near a railway station. Check if the parking charges are in direct proportion to the parking time. View Answer

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. View Answer

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? View Answer

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

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? View Answer

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? View Answer

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? View Answer

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? View Answer

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. View Answer

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

**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. View Answer

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? View Answer

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.(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°? View Answer

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? View Answer

Q5 – 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? View Answer

Q6 – 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? View Answer

Q7 – 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? View Answer

Q8 – 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? View Answer

Q9 – 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? View Answer

Q10 – 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? View Answer

Q11 – 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? View Answer

## End Note

In the article, we have shared solutions for ncert exercises for class 8 maths for direct and indirect proportion chapter. Students can click to respective chapters and refer to the right solution. We advise students to refer to them as clearing their concepts, and matching their solutions. Student should not use them to copy solutions for their homework and instead should try to solve homework on own, as it will impact their learning process.

In case you have any doubts regarding solution, or need further clarification, you can write to us. You can also reach out to us, in case you have doubt in other text books’ problems or school exam papers. We will be glad to assist you in helping with your doubt.

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