- If 18 binders bind 900 books in 10 days.

- Binders required to bind 660 books in 12 days can be figure out in this way.

## Explanation

Three given entities here are

- Books
- Days
- Binders

To determine the relation here, let suppose; Binders required to bind 660 books in 12 days = y

__Case I__

Books Binders

900Â Â Â Â Â Â Â Â Â Â Â Â 18

660Â Â Â Â Â Â Â Â Â Â y

- More books mean more binders.
- Less books mean less binders.

This clearly indicates that there is direct relation.

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

900 : 660 :: 18 : y ________ (i)

__Case II__

Days Binders

10Â Â Â Â Â Â Â Â Â Â Â Â Â Â 18

12Â Â Â Â Â Â Â Â Â Â Â Â y

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

This clearly indicates that there is inverse relation.

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

12 : 10 :: 18 : y ________ (ii)

By (i) and (ii)

900 : 660 :: 18 : y

12 : 10

900 x 12 x y = 660 x 10 x 18 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 11)

## To Find

Binders required to bind 660 books in 12 days = ?

## Solution

__Method I__

Let suppose

Binders required to bind 660 books in 12 days = y

Books Days Binders

900Â Â Â Â Â Â Â Â Â Â Â Â 10Â Â Â Â Â Â Â Â Â Â Â Â Â Â 18

660 Â Â Â Â Â Â Â Â Â Â Â 12Â Â Â Â Â Â Â Â Â Â Â Â y

- Relation between books and binders is direct.
- Relation between days and binders is inverse.

So

900 : 660 :: 18 : y

12 : 10

900 x 12 x y = 660 x 10 x 18

10800y = 118800

y = 118800/10800

y = 11

**Binders required to bind 660 books in 12 days = 11 binders answer**

__Method II__

Binders required to bind 900 books in 10 days = 18 binders

Binders required to bind 900 books in 1 day = (18 x 10) binders

Binders required to bind 900 books in 1 day = 180 binders

Binders required to bind 1 book in 1 day = 180/900 binders

Binders required to bind 1 book in 1 day = 1/5 binders

Binders required to bind 660 books in 1 day = 660/5 binders

Binders required to bind 660 books in 1 day = 132 binders

Binders required to bind 660 books in 12 days = 132/12 binders

Binders required to bind 660 books in 12 days = 11 binders

**Binders required to bind 660 books in 12 days = 11 binders answer**

### Conclusion

If 18 binders bind 900 books in 10 days, 11 binders will be required to bind 660 books in 12 days.