Maharashtra Board Solutions Class 7-Maths (Practice Set 38): Chapter 9- Direct Proportion and Inverse Proportion

Class 7: Maths Chapter 9 solutions. Complete Class 7 Maths Chapter 9 Notes.

Maharashtra Board Solutions Class 7-Maths (Practice Set 38): Chapter 9- Direct Proportion and Inverse Proportion

Maharashtra Board 7th Maths Chapter 9, Class 7 Maths Chapter 9 solutions

Question 1.
Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?
Solution:
Let 6 workers take x days and 15 workers take y days to weed the field.
The number of workers and the time required to weed the field are in inverse proportion.
∴ 6 × x = 5 × 12
∴ x=5×126
∴ x = 10 days
Also, 15 × y = 5 × 12
∴ y=5×1215
= 4 days
∴ 6 workers will take 10 days and 15 workers will take 4 days to weed the field.

Question 2.
Mohanrao took 10 days to finish a book, reading 40 pages every day. How many pages must he read in a day to finish it in 8 days?
Solution:
Let Mohanrao read x pages every day to finish the book in 8 days.
The number of pages read per day and the days required to finish the book are in inverse proportion.
∴ 8 × x = 10 × 40
∴ x=10×408
= 50
∴ Mohanrao will have to read 50 pages every day to finish the book in 8 days.

Question 3.
Mary cycles at 6 km per hour. How long will she take to reach her Aunt’s house which is 12 km away? If she cycles at a speed of 4 km/hr, how long would she take?
Solution:
Speed of the cycle = 6 km / hr
Distance travelled to reach her Aunt’s house = 12 km
∴  Time required = Distance travelled  Speed 
= 126
= 2 hours
Let the time required when the speed of the cycle is 4 km/hr be x hours.
The speed of the cycle and the time required to travel the same distance are in inverse proportion.
∴ 4 × x = 6 × 2
∴ x=6×24 = 3 hours
∴ Mary will require 2 hours if she is cycling at 6 km/hr and 3 hours if she is cycling at 4 km/hr to reach her Aunt’s house.

Question 4.
The stock of grain in a government warehouse lasts 30 days for 4000 people. How many days will it last for 6000 people?
Solution:
Let the stock of grain last for x days for 6000 people.
The number of people and the days for which stock will last are in inverse proportion.
∴ 6000 × x = 4000 × 30
∴ x=4000×306000=20
∴ The stock of grain will last for 20 days for 6000 people.

Intext Questions and Activities

Question 1.
Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.
(Textbook pg. no. 65 and 66)
i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.

ii. The sweets shop near the school gave 90 laddoos for the picnic.
If 45 students go for the picnic, each will get___laddoos.
If 30 students go for the picnic, each will get___laddoos.
The number of students and that of laddoos each one gets are in___proportion.

iii. The farm is 120 km away from the school.
The bus went to the farm at a speed of 40 km per hour and took___hours.
On the return trip, the speed was 60 km per hour. Therefore, it took___hours.
The speed of the bus and the time it takes are in___proportion.

iv. The farmer picked 180 bors from his trees.
He gave them equally to 45 students. Each student got___bors.
Had there been 60 students, each would have got___bors.
The number of students and the number of bors each one gets are in___proportion.
Solution:
i. Rs 2700, Rs 3000, direct
ii. 2,3, inverse
iii. 3,2, inverse
iv. 4,3, inverse

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Maharashtra Board Solutions Class 7-Maths (Practice Set 38): Chapter 9- Direct Proportion and Inverse Proportion

Download PDF: Maharashtra Board Solutions Class 7-Maths (Practice Set 38): Chapter 9- Direct Proportion and Inverse Proportion PDF

Chapterwise Maharashtra Board Solutions Class 7 Maths :

• Chapter 1- Geometrical Constructions (Practice Set 1)
• Chapter 1- Geometrical Constructions (Practice Set 2)
• Chapter 1- Geometrical Constructions (Practice Set 3)
• Chapter 1- Geometrical Constructions (Practice Set 4)
• Chapter 1- Geometrical Constructions (Practice Set 5)
• Chapter 1- Geometrical Constructions (Practice Set 6)
• Chapter 1- Geometrical Constructions (Practice Set 7)
• Chapter 2- Multiplication and Division of Integers (Practice Set 8)
• Chapter 2- Multiplication and Division of Integers (Practice Set 9)
• Chapter 3- HCF and LCM (Practice Set 10)
• Chapter 3- HCF and LCM (Practice Set 11)
• Chapter 3- HCF and LCM (Practice Set 12)
• Chapter 3- HCF and LCM (Practice Set 13)
• Chapter 3- HCF and LCM (Practice Set 14)
• Chapter 4- Angles and Pairs of Angles (Practice Set 15)
• Chapter 4- Angles and Pairs of Angles (Practice Set 16)
• Chapter 4- Angles and Pairs of Angles (Practice Set 17)
• Chapter 4- Angles and Pairs of Angles (Practice Set 18)
• Chapter 4- Angles and Pairs of Angles (Practice Set 19)
• Chapter 4- Angles and Pairs of Angles (Practice Set 20)
• Chapter 4- Angles and Pairs of Angles (Practice Set 21)
• Chapter 5- Operations on Rational Numbers (Practice Set 22)
• Chapter 5- Operations on Rational Numbers (Practice Set 23)
• Chapter 5- Operations on Rational Numbers (Practice Set 24)
• Chapter 5- Operations on Rational Numbers (Practice Set 25)
• Chapter 6- Indices (Practice Set 26)
• Chapter 6- Indices (Practice Set 27)
• Chapter 6- Indices (Practice Set 28)
• Chapter 6- Indices (Practice Set 29)
• Chapter 6- Indices (Practice Set 30)
• Chapter 7- Joint Bar Graph (Practice Set 31)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 32)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 33)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 34)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 35)
• Chapter 8- Algebraic Expressions and Operations on them (Practice Set 36)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 37)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 38)
• Chapter 9- Direct Proportion and Inverse Proportion (Practice Set 39)
• Chapter 10- Bank and Simple Interest (Practice Set 40)
• Chapter 10- Bank and Simple Interest (Practice Set 41)
• Chapter 11- Circle (Practice Set 42)
• Chapter 11- Circle (Practice Set 43)
• Chapter 12- Perimeter and Area (Practice Set 44)
• Chapter 12- Perimeter and Area (Practice Set 45)
• Chapter 12- Perimeter and Area (Practice Set 46)
• Chapter 12- Perimeter and Area (Practice Set 47)
• Chapter 13- Pythagoras Theorem (Practice Set 48)
• Chapter 13- Pythagoras Theorem (Practice Set 49)
• Chapter 14- Algebraic Formulae – Expansion of Squares (Practice Set 50)
• Chapter 14- Algebraic Formulae – Expansion of Squares (Practice Set 51)
• Chapter 14- Algebraic Formulae – Expansion of Squares (Practice Set 52)
• Chapter 14- Algebraic Formulae – Expansion of Squares (Practice Set 53)
• Chapter 15- Statistics (Practice Set 54)
• Chapter 14- Statistics (Practice Set 55)