Maharashtra Board Solutions Class 8-Maths (Practice Set 7.3): Chapter 7- Variation

Class 8: Maths Chapter 7 solutions. Complete Class 8 Maths Chapter 7 Notes.

Maharashtra Board Solutions Class 8-Maths (Practice Set 7.3): Chapter 7- Variation

Maharashtra Board 8th Maths Chapter 7, Class 8 Maths Chapter 7 solutions

Question 1.
Which of the following statements are of inverse variation?
i. Number of workers on a job and time taken by them to complete the job.
ii. Number of pipes of same size to fill a tank and the time taken by them to fill the tank.
iii. Petrol filled in the tank of a vehicle and its cost.
iv. Area of circle and its radius.
Solution:
i. Let, x represent number of workers on a job, and y represent time taken by workers to complete the job.
As the number of workers increases, the time required to complete the job decreases.
∴ x∝1y

ii. Let, n represent number of pipes of same size to fill a tank and t represent time taken by the pipes to fill the tank.
As the number of pipes increases, the time required to fill the tank decreases.
∴ n∝1t

iii. Let, p represent the quantity of petrol filled in a tank and c represent the cost of the petrol.
As the quantity of petrol in the tank increases, its cost increases.
∴ p ∝ c

iv. Let, A represent the area of the circle and r represent its radius.
As the area of circle increases, its radius increases.
∴ A ∝ r
∴ Statements (i) and (ii) are examples of inverse variation.

Question 2.
If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
Solution:
Let, n represent the number of workers building the wall and t represent the time required.
Since, the number of workers varies inversely with the time required to build the wall.
∴ n∝1t
∴ n=k×1t
where k is the constant of variation
∴ n × t = k …(i)
15 workers can build a wall in 48 hours,
i.e., when n = 15, t = 48
∴ Substituting n = 15 and t = 48 in (i), we get
n × t = k
∴ 15 × 48 = k
∴ k = 720
Substituting k = 720 in (i), we get
n × t = k
∴ n × t = 720 …(ii)
This is the equation of variation.
Now, we have to find number of workers required to do the same work in 30 hours.
i.e., when t = 30, n = ?
∴ Substituting t = 30 in (ii), we get
n × t = 720
∴ n × 30 = 720
∴ n = 72030
∴ n = 24
∴ 24 workers will be required to build the wall in 30 hours.

Question 3.
120 bags of half litre milk can be filled by a machine within 3 minutes find the time to fill such 1800 bags?
Solution:
Let b represent the number of bags of half litre milk and t represent the time required to fill the bags.
Since, the number of bags and time required to fill the bags varies directly.
∴ b ∝ t
∴ b = kt …(i)
where k is the constant of variation.
Since, 120 bags can be filled in 3 minutes
i.e., when b = 120, t = 3
∴ Substituting b = 120 and t = 3 in (i), we get
b = kt
∴ 120 = k × 3
∴ k = 1203
∴ k = 40
Substituting k = 40 in (i), we get
b = kt
∴ b = 40 t …(ii)
This is the equation of variation.
Now, we have to find time required to fill 1800 bags
∴ Substituting b = 1800 in (ii), we get
b = 40 t
∴ 1800 = 40 t
∴ t = 180040
∴ t = 45
∴ 1800 bags of half litre milk can be filled by the machine in 45 minutes.

Question 4.
A car with speed 60 km/hr takes 8 hours to travel some distance. What should be the increase in the speed if the same distance is
to be covered in 712 hours?
Solution:
Let v represent the speed of car in km/hr and t represent the time required.
Since, speed of a car varies inversely as the time required to cover a distance.
∴ v∝1t
∴ v=k×1t
where, k is the constant of variation.
∴ v × t = k …(i)
Since, a car with speed 60 km/hr takes 8 hours to travel some distance.
i.e., when v = 60, t = 8
∴ Substituting v = 60 and t = 8 in (i), we get
v × t = k
∴ 60 × 8 = t
∴ k = 480
Substituting k = 480 in (i), we get
v × t = k
∴ v × t = 480 …(ii)
This is the equation of variation.
Now, we have to find speed of car if the same distance is to be covered in 712 hours.
i.e., when t = 712 = 7.5 , v = ?
∴ Substituting, t = 7.5 in (ii), we get
v × t = 480
∴ v × 7.5 = 480
v=4807.5=480075
∴ v = 64
The speed of vehicle should be 64 km/hr to cover the same distance in 7.5 hours.
∴ The increase in speed = 64 – 60
= 4km/hr
∴ The increase in speed of the car is 4 km/hr.

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Maharashtra Board Solutions Class 8-Maths (Practice Set 7.3): Chapter 7- Variation

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Chapterwise Maharashtra Board Solutions Class 8 Maths :

• Chapter 1- Rational and Irrational Numbers (Practice Set 1.1)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.2)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.3)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.4)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.1)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.2)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.3)
• Chapter 3- Indices and Cube Root (Practice Set 3.1)
• Chapter 3- Indices and Cube Root (Practice Set 3.2)
• Chapter 3- Indices and Cube Root (Practice Set 3.3)
• Chapter 4- Altitudes and Medians of a Triangle (Practice Set 4.1)
• Chapter 5- Expansion Formulae (Practice Set 5.1)
• Chapter 5- Expansion Formulae (Practice Set 5.2)
• Chapter 5- Expansion Formulae (Practice Set 5.3)
• Chapter 5- Expansion Formulae (Practice Set 5.4)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.1)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.2)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.3)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.4)
• Chapter 7- Variation (Practice Set 7.1)
• Chapter 7- Variation (Practice Set 7.2)
• Chapter 7- Variation (Practice Set 7.3)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.1)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.2)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.3)
• Chapter 9- Discount and Commission (Practice Set 9.1)
• Chapter 9- Discount and Commission (Practice Set 9.2)
• Chapter 10- Division of Polynomials (Practice Set 10.1)
• Chapter 10- Discount and Commission (Practice Set 10.2)
• Chapter 11- Statistics (Practice Set 11.1)
• Chapter 11- Statistics (Practice Set 11.2)
• Chapter 11- Statistics (Practice Set 11.3)
• Chapter 12- Equations in One Variable (Practice Set 12.1)
• Chapter 12- Equations in One Variable (Practice Set 12.2)
• Chapter 13- Congruence of Triangles (Practice Set 13.1)
• Chapter 13- Congruence of Triangles (Practice Set 13.2)
• Chapter 14- Compound Interest (Practice Set 14.1)
• Chapter 14- Compound Interest (Practice Set 14.2)
• Chapter 15- Area (Practice Set 15.1)
• Chapter 15- Area (Practice Set 15.2)
• Chapter 15- Area (Practice Set 15.3)
• Chapter 15- Area (Practice Set 15.4)
• Chapter 15- Area (Practice Set 15.5)
• Chapter 15- Area (Practice Set 15.6)
• Chapter 16- Surface Area and Volume (Practice Set 16.1)
• Chapter 16- Surface Area and Volume (Practice Set 16.2)
• Chapter 16- Surface Area and Volume (Practice Set 16.3)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.1)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.2)