# NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.2 Part 1

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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.

Answer:

(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 work and more workers will take less time to complete the same work.

(ii) Time and distance covered in direct proportion.

(iii) It is a direct proportion because more are of cultivated land will yield more crops.

(iv) Time and speed are 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 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:

No. of winners | |||||||

Prize for each winner (in Rs) | ____ | ____ | ____ | ____ | ___ |

Answer:

Here, number of winners and prize money are in inverse proportion because winners are increasing, prize money is decreasing.

When the number of winners are 4, each winner will get

When the number of winners are , each winner will get

When the number of winners are , each winner will get

When the number of winners are , each winner will get =

When the number of winners are , each winner will get