Inverse proportion :
Inverse proportion is a situation where an increases in one quantity causes a corresponding decreases in the other quantity.
(or)
Inverse proportion is a situation where an decreases in one quantity causes a corresponding increases in the other quantity.
Problem 1 :
6 pumps are required to fill a water sump in 1 hr 30 minutes. What will be the time taken to fill the sump if one pump is switched off ?
Solution :
Let ‘x’ be the required time taken.
As the number of pumps increases the time taken to fill the sump will be less.
It comes under inverse proportion.
90 ⋅ 6 = x ⋅ 5
540 = x ⋅ 5
540/5 = x
108 = x
108/60 = 1 hour 48 min.
Therefore, the time taken to fill the sump is 1 hour 48 min.
Problem 2 :
A farmer has enough food for 144 ducks for 28 days. If he sells 32 ducks, how long will the food last ?
Solution :
Let the required number of days be ‘x’.
As the number of ducks decreases the food will last for more days.
It comes under inverse proportion.
28 ⋅ 144 = x ⋅ 112
4032 = x ⋅ 112
4032/112 = x
36 = x
Therefore, the food last for 36 days.
Problem 3 :
If takes 60 days for 10 machines to dig a hole. Assuming that all machines work at the same speed, how long will it take 30 machines to dig the same hole ?
Solution :
Let the number of days required be x.
As the number of machines increases it takes less days to complete the work.
It comes under inverse proportion.
10 ⋅ 60 = 30 ⋅ x
600 = 30 ⋅ x
600/30 = x
20 = x
Therefore, it takes 20 days to dig the hole.
Problem 4 :
Forty students stay in a hostel. They had food stock for 30 days. If the students are doubled then for how many days the stock will last ?
Solution :
Let ‘x’ be the required number of days.
As the number of students increases the food last for less number of days.
It comes under inverse proportion.
30 ⋅ 40 = x ⋅ 80
1200 = x ⋅ 80
1200/80 = x
15 = x
Therefore, the food stock lasts for 15 days.
Problem 5 :
Meena had enough money to send 8 parcels each weighing 500 grams through a courier service. What would be the weight of each parcel, if she has to send 40 parcels for the same money ?
Solution :
Let the weight of parcel be ‘x’ grams.
As the number of parcels increases weight of a parcel decreases.
It comes under inverse proportion.
8 ⋅ 500 = 40 ⋅ x
4000 = 40 ⋅ x
4000/40 = x
100 = x
Therefore, the weight of each parcel is 100 grams.
Problem 6 :
If takes 120 minutes to weed a garden with 6 gardeners if the same work is to be done in 30 minutes, how many more gardeners are needed ?
Solution :
Let the number of gardeners needed be ‘x’.
As the number of gardeners increases the time decreases.
It comes under inverse proportion.
6 ⋅ 120 = x ⋅ 30
720 = x ⋅ 30
720/30 = x
24 = x
To complete the work in 30 min gardeners needed = 24
Already existing gardeners = 6
= 24 – 6
= 18
Therefore, 18 more gardeners are needed.
Problem 7 :
Heena goes by bi-cycle to her school every day. Her average speed is 12 km/hr and she reaches school in 20 minutes. What is the increase in speed, if she reaches the school in 15 minutes ?
Solution :
Let the speed to reach school in 15 minutes be `x’.
It comes under inverse proportion.
If she reaches the school in 15 minutes the speed = 16 km/hr
Already running with 12 km/hr
Increased speed = 16 – 12 = 4 km/hr
Therefore, the increase in speed = 4 km/hr.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jan 17, 22 10:45 AM
Trigonometry Word Problems Worksheet with Answers
Jan 17, 22 10:41 AM
Trigonometry Word Problems with Solutions
Jan 16, 22 11:56 PM
Writing Numbers in Words Worksheet