Question

Which of the following statements are of inverse variation ?(1) Number of workers on a job and time taken by them to complete the job.(2) Number of pipes of same size to fill a tank and the time taken by them to fill the tank.(3) Petrol filled in the tank of a vehicle and its cost(4) Area of circle and its radius.

Answer 1

Answer:

Number of workers on a job and time taken by them to complete the job

Number of pipes of same size to fill a tank and the time taken by them to fill the tank

Step-by-step explanation:

following statements are of inverse variation :

1. Number of workers on a job and time taken by them to complete the job.

As number of Workers increase time Taken is Decreased

Time Taken by Workers = Total Work Done / number of Workers

2.  Number of pipes of same size to fill a tank and the time taken by them to fill the tank.

As Number of pipes increase time Taken is Decreased

Time Taken by pipes = Tank Filled / Number of Pipes

Following Statements are of direct proportion :

Petrol filled in the tank of a vehicle and its cost

Cost = Petrol filled   * Petrol Price

Area of circle and its radius.

Area of circle ∝ Radius²

Answer 2

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CONCEPT TO BE IMPLEMENTED

DIRECT VARIATION

Direct variation is a linear relationship between two variables such that when one variable increases, the other increases and when one variable decreases , the other decreases

INVERSE VARIATION

Inverse variation is a relationship between two variables. The two quantities are said to be in inverse variation such that when one quantity increases, the other decreases.

TO CHOOSE THE CORRECT OPTION

TO choose a statement stating inverse variation :

(1) Number of workers on a job and time taken by them to complete the job

(2) Number of pipes of same size to fill a tank and the time taken by them to fill the tank

(3) Petrol filled in the tank of a vehicle and its cost

(4) Area of circle and its radius

CALCULATION

CHECKING FOR OPTION : 1

Here if in order to complete a job if Number of workers on a job increases then time taken by them to complete the job decreases

Hence it is an INVERSE VARIATION

CHECKING FOR OPTION (2)

In order to fill a tank if the Number of pipes of same size increases then time taken by them to fill the tank decreases

Hence it is a INVERSE VARIATION

CHECKING FOR OPTION (3)

In order to fill tank of a vehicle if amount of petrol increases then the cost also increases

Hence it is a DIRECT VARIATION

CHECKING FOR OPTION (4)

If r is the radius of a circle

$\sf{Then \: area \: = \pi {r}^{2} }$

So the area of a circle increases when the radius of the circle increases

Hence it is a DIRECT VARIATION

RESULT

The correct statement for Inverse Variation are :

(1) Number of workers on a job and time taken by them to complete the job

(2) Number of pipes of same size to fill a tank and the time taken by them to fill the tank

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