Class 8, Maths, Chapter 13, Exercise 13.2 Solutions
Q.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.
Ans: (i) Direct inverse, These are in inverse proportion because if there are more
workers, then it will take lesser time to complete that job.
(ii) Non-Direct inverse, because we may cover more distance with a uniform speed. It is a direct Proportion.
(iii) Non-Direct inverse, because in more area, more quantity of crop may be harvested. It is a direct Proportion.
(iv) Direct inverse, because with more speed, we may complete a certain distance in a lesser time.
(v) Direct inverse, because if the population in increasing, then area of the land per person will be decreasing accordingly.
Q.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?
Ans: Given, Fixed prize money = Rs 1,00,000
(i) If winner is 4, then prize money $=\frac{1,00,000}{4}=Rs\,\,25,000$
(ii) If winner is 5, then prize money $=\frac{1,00,000}{5}=Rs\,\,20,000$
(iii) If winner is 8, then prize money $=\frac{1,00,000}{8}=Rs\,\,12,500$
(iv) If winner is 10, then prize money $=\frac{1,00,000}{10}=Rs\,\,10,000$
(v) If winner is 20, then prize money $=\frac{1,00,000}{20}=Rs\,\,5,000$
Thus, the number of winners and amount given to an individual winner is inversely proportional.
Q.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.
(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°?
Q.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?
Q.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?
Q.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?
Q.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?
Q.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?
Q.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?
Q.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?
Q.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?
