Question

The information about numbers of workers and number of days to complete a work is given in the following table. Complete the table.

Number of workers	30	20		10
Days	6	9	12		36

Answer 1

It can be observed from the given table that if the number of workers is increased from 20 to 30, then the number of days to complete the work decreases from 9 days to 6 days. So, the number of workers and the number of days to complete a work are in inverse variation.

Let the number of workers be y and the number of days to complete a work be x.

Here, y inversely varies as x, i.e., `y  α  1/z`.

\[\therefore y = \frac{k}{x}\] , where k constant of variation

⇒ x × y = k

When y = 30, x = 6.

∴ k = 6 × 30

= 180

So, the equation of variation is xy = 180.

When x = 12,

12y = 180

y = `180/12`

⇒ y = 15

When y = 10,

10x = 180

x = `180/10`

⇒ x = 18

When x = 36

36y = 180

y = `180/36`

⇒ y = 5

The complete table is given below.

Number of workers	30	20	15	10	5
Days	6	9	12	18	36