Chapter 13: Direct and Inverse Proportions

(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) 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 in 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.

Here, 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 =100000/4 = Rs. 25,000

When the number of winners is 5, each winner will get =100000/5 = Rs. 20,000

When the number of winners is 8, each winner will get =100000/8 = Rs. 12,500

When the number of winners is 10, each winner will get = 100000/10 = Rs. 10,000

When the number of winners is 20, each winner will get = 100000/20 = Rs. 5,000

Here, 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 degree.

When the number of spokes is 8, then the angle between a pair of consecutive spokes = 360/8 = 45 degree

When the number of spokes is 10, then the angle between a pair of consecutive spokes = 360/10= 36 degree.

When the number of spokes is 12, then the angle between a pair of consecutive spokes = 360/12 = 30 degree.

(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 degree.

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

Each child gets = 5 sweets

24 children will get 24×5 = 120 sweets.

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 = 120/20 = 6 sweets

Let the number of days be x.

Total number of animals = 20+10 = 30

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

x = 4

Hence, the food will last for four days.

Let the time taken to complete the job be x.

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

¾ = x/4

3×4 = 4x

x = 3×4/4

x = 3

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

Let the number of boxes be x.

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

12/20 = x/25

12×25 = 20x

x = 12×25/20 = 15

Hence, 15 boxes would be filled.

Let the number of machines required be x.

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

63/54 = x/42

63×42 = 54x

x = 63×42/54

x= 49

Hence, 49 machines would be required.

Let the number of hours be x.

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

60/80 = x/2

60×2 = 80x

x = 60×2/80

(i) Let the number of days be x.

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

2/1 = x/3

6 = x

Or

x = 6 days

(ii) Let the number of persons be x.

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

2/x = 1/3

6 = x

Or

x = 6 persons