Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Ex 4.2
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Ex 4.2
Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Ex 4.2
Question 1.
Fill in the blanks
(i) 16 taps can fill a petrol tank in 18 minutes. The time taken for 9 taps to fill the same tank will be ___ minutes.
(ii) If 40 workers can do a project work in 8 days, then ____ workers can do it in 4 days.
Solutions:
(i) 32
(ii) 80
Question 2.
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
Time taken in minutes 1 hr. 48m
Question 3.
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.
∴ They are in inverse proportion. x1y1 = x2y2
The food lasts for 36 days
Question 4.
It 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
∴ They are in inverse proportion, x1y1 = x2y2
It takes 20 days to dig the hole
Question 5.
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 the required number of days be x.
As the number of students increases the food last for less number of days
∴ They are in inverse proportion.
The food stock lasts for 15 days
Question 6.
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 parcel for the same money?
Solution:
Let the required weight of the parcel be x grams.
As the number of parcels increases weight of a parcel decreases.
∴ They are in inverse proportion.
Weight of each parcel = 100 grams
Question 7.
It takes 120 minutes to weed a garden with 6 gardeners. If the same work is to be done in 30minutes, how many more gardeners are needed?
Solution:
Let the, number of gardeners needed be x.
As the number of gardeners increases the time decreases. They are in inverse proportion,
x1y1 = x2y2
∴ To complete the work in 30 min gardeners needed = 24
Already existing gardeners = 6
∴ More gardeners needed = 24 – 6 = 18
18 more gardeners are needed
Question 8.
Neelaveni goes by bicycle to her school every day. Her average speed is 12km/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 min be x
∴ They are in inverse proportion x1y1 = x2 y2
If she reaches in 15 min the speed = 16 km/hr
Already running with 12 km / hr
∴ Increased speed = 16 – 12 = 4km / hr
Increase in speed = 4 km / hr
Question 9.
A toy company requires 36 machines to produce car toys in 54 days. How many machines would be required to produce the same number of car toys in 81 days?
Solution:
Let the required number of machines be x
As the number of machines increases number of days required decreases.
∴ 24 machines would be required
Objective Type Questions
Question 10.
12 cows can graze a field for 10 days. 20 cows can graze the same field for ____ days
(i) 15
(ii) 18
(iii) 6
(iv) 8
Solution:
(iii) 6
Hint:
Question 11.
4 typists are employed to complete a work in 12 days. If two more typists are added, they will finish the same work in days
(i) 7
(ii) 8
(iii) 9
(iv) 10
Solution:
(ii) 8
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