- Introduction
- |
- Direct Proportion
- |
- How to Solve Direct Proportion Problems
- |
- Inverse proportion
- |
- How to Solve Inverse Proportion Problems

In this page we have *NCERT book Solutions for Class 8th Maths:Direct and Inverse Proportion Chapter 13 * for
EXERCISE 1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

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.

- Here more the number of workers for the job, less time will be taken to complete the job, So inverse proportion
- Here more the distance to be travelled , more time will be taken at constant speed, so direct proportion
- Here more the area, more the crop harvested, so direct proportion
- Here more the speed, less time taken for fixed journey, so inverse proportion
- Again same inverse proportion

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?

Number of winners |
1 |
2 |
4 |
5 |
8 |
10 |
20 |

Prize for each winner in Rs |
1,00,000 |
50,000 |

Here more the winner, less will be the prize money for each winner, so number of winner and prize money are in inverse proportion

Also from the table

1×10,0000 =2×50,000= 100,000

Number of winners |
1 |
2 |
4 |
5 |
8 |
10 |
20 |

Prize for each winner in Rs |
1,00,000 |
50,000 |
a |
b |
c |
d |
e |

4a=100,000

a=25,000

5b=100,000

b=20,000

8c=100,000

c=125,00

10d=100,000

d=10,000

20e=100,000

e=50,00

So result table looks like

Number of winners |
1 |
2 |
4 |
5 |
8 |
10 |
20 |

Prize for each winner in Rs |
1,00,000 |
50,000 |
25,000 |
20,000 |
12,500 |
10,000 |
5,000 |

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 spokes |
4 |
6 |
8 |
10 |
12 |

Angle between two consecutive spoke |
90^{0} |
60^{0} |

- Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
- Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
- How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?

In the given table, we see that

4 × 90= 6 × 60= 360

So number of spokes and angle between are in inverse proportion

Number of spokes |
4 |
6 |
8 |
10 |
12 |

Angle between two consecutive spoke |
90^{0} |
60^{0} |
a |
b |
c |

10b=360 => b=36

12c=360 => c=30

Number of spokes |
4 |
6 |
8 |
10 |
12 |

Angle between two consecutive spoke |
90^{0} |
60^{0} |
45^{0} |
36^{0} |
30^{0} |

- As with increasing number of spokes the angle is decreasing so they are in inverse proportion.
- For 15 spokes
15x=360 => x=24
^{0}

- Let y be the number of spokes required, then
40y=360

y=9

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?

Let x be the amount of sweet if the number of children is 20

20x= 24×5

x=6

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?

No of animals and days last are in inverse proportion as on increasing the animals, food will be consumed fast and it will finish in less number of days

Let x be the days for 30 animals

30x= 120

x=4 days

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?

Numbers of person and days to complete are in inverse proportion as on increasing the people, fewer days will be required

Let y be days required for 3 person

3y= 12

x=4 days

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?

20x=25× 12

x=15 boxes

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?

Let x be the machines

42×63= 54x

x=49 machines

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?

2×60=80a

a=1.5 hours

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?

- 2×3= 1y
=> y =6 days

- Using same calculation 6 persons are required to fit the windows in 1 day.

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?

8×45= 9a

a=40 minutes

Download this assignment as pdf

Class 8 Maths Class 8 Science