- 39 persons can repair a road in 12 days working 5 hours a day.

- The days required to complete the work by 30 persons working 6 hours a day can be figure out in this way.

## Explanation

Three given entities here are

- Person
- Hours
- Days

To determine the relation here, let suppose; The days required to complete the work by 30 persons working 6 hours a day = y

__Case I__

Person Days

39 12

30 y

- More persons mean less days to get the job done.
- Less persons mean more days to complete the job.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

39 : 30 :: y : 12 ________ (i)

__Case II__

Hours Days

5 12

6 y

- Less hours mean more days.
- More hours mean less days.

This clearly indicates that there is also inverse relation.

Direct/Indirect relation tells how the equation will be written.

5 : 6 :: y : 12 ________ (ii)

By (i) and (ii)

39 : 30 :: y : 12

5 : 6

39 x 5 x 12 = 30 x 6 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 13)

## To Find

The days required to complete the work by 30 persons working 6 hours a day = ?

## Solution

__Method I__

Let suppose

The days required to complete the work by 30 persons working 6 hours a day = y

Person Hours Days

39 5 12

30 6 y

- Relation between persons and days is inverse.
- Relation between hours and days is also inverse so;

39 : 30 :: y : 12

5 : 6

39 x 5 x 12 = 30 x 6 x y

2340 = 180y

2340/180 = y

13 = y

y = 13 days

**The days required to complete the work by 30 persons working 6 hours a day**** = 13 days answer**

__Method II__

The days required to complete the work by 39 persons working 5 hours a day** = **12 days

The days required to complete the work by 39 persons working 1 hours a day** = **(12 x 5) days

The days required to complete the work by 1 person working 1 hours a day** = **(12 x 5 x 39) days

The days required to complete the work by 1 persons working 6 hours a day** = **2340/6 days

The days required to complete the work by 1 persons working 6 hours a day** = **390 days

The days required to complete the work by 30 persons working 6 hours a day** = **390/30 days

The days required to complete the work by 30 persons working 6 hours a day** = **13 days

**The days required to complete the work by 30 persons working 6 hours a day**** = 13 days answer**

### Conclusion

39 persons can repair a road in 12 days working 5 hours a day. In 13 days, 30 persons working 6 hours a day can complete the work.