Which of the following statements are of inverse variation?i. Number

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.
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. \(\therefore x\propto \cfrac{1}{y}\) 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. \(\therefore n\propto \cfrac{1}{t}\) 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.

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.

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.

\(\therefore x\propto \cfrac{1}{y}\)

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.

\(\therefore n\propto \cfrac{1}{t}\)

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.