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*∝1/y

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∝1/t

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.

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 = 120/3

∴ 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 = 1800/40

∴ t = 45

∴ 1800 bags of half litre milk can be filled by the machine in 45 minutes.

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.