- Some persons can do a piece of work in 12 days.

- Days taken by two times the number of such person to do half of the work will be figure out in this way.

## Explanation

Two given entities here are

- Person
- Days

To determine the relation here, let suppose; Days taken by two times the number of such person to complete the work = y

__Case__

Let suppose

Some persons = 10

Two times the number of such person = 20

Person Days

10 12

20 y

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

This clearly indicates that there is inverse relation.

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

10 : 20 :: y : 12 ________ (i)

20 x y = 10 x 12 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 6 and to do half of the work = 6/2 = 3 days)

## To Find

Days taken by two times the number of such person to do half of the work = ?

## Solution

__Method I__

Let suppose

Days taken by two times the number of such person to complete the work = y

Person Days

10 12

20 y

- Relation between person and days is inverse.

So

10 : 20 :: y : 12

20 x y = 10 x 12

20y = 120

y = 120/20

y = 6 days

Days taken by two times the number of such person to complete the work = 6 days

Days taken by two times the number of such person to do half of the work = 6/2

**Days taken by two times the number of such person to do half of the work = 3 days answer**

__Method II__

Let suppose

Some persons = 10

Two times the number of such person = 20

Days taken by 10 persons to complete the work = 12 days

Days taken by 1 person to complete the work = (12 x 10) days

Days taken by 1 person to complete the work = 120 days

Days taken by 20 person to complete the work = 120/20 days

Days taken by 20 person to complete the work = 6 days

Days taken by two times the number of such person to complete the work = 6 days

Days taken by two times the number of such person to do half of the work = 6/2

**Days taken by two times the number of such person to do half of the work = 3 days answer**

### Conclusion

Some persons can do a piece of work in 12 days. Two times the number of such person will do half of that work in 3 days.