Practice Set 7.3 8th Std Maths Answers Chapter 7 Variation
Question 1
Maharashtra Board Solution
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 & Step-by-Step Answer:
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. ∴
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.
∴
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
Maharashtra Board Solution
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 & Step-by-Step Answer:
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. ∴ ∴ 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 = ∴ n = 24 ∴ 24 workers will be required to build the wall in 30 hours.
Question 3
Maharashtra Board Solution
120 bags of half litre milk can be filled by a machine within 3 minutes find the time to fill such 1800 bags?
Solution & Step-by-Step Answer:
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 = ∴ 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 = ∴ t = 45 ∴ 1800 bags of half litre milk can be filled by the machine in 45 minutes.
Question 4
Maharashtra Board Solution
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 hours?
Solution & Step-by-Step Answer:
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. ∴ ∴ 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 hours. i.e., when t = = 7.5, v = ? ∴ Substituting, t = 7.5 in (ii), we get v × t = 480 ∴ v × 7.5 = 480 ∴ 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.