#### 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 |

#### Solution

It can be observed from the given table that if 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 worker and 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. \[y \propto \frac{1}{x}\].

\[\therefore y = \frac{k}{x}\] , 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 = 15

When y = 10,

10x = 180

⇒ x = 18

When x = 36

36y = 180

⇒ y = 5

The complete table is given below.

Number of workers | 30 | 20 | 15 |
10 | 5 |

Days | 6 | 9 | 12 | 18 |
36 |