- 4 mat-weavers can weave 4 mats in 4 days.

- Mats woven by 8 mat-weavers in 8 days can be figure out in this way.

## Explanation

Three given entities here are

- Mat Weavers
- Days
- Mats

To determine the relation here, let suppose; Mats woven by 8 mat-weavers in 8 days = y

__Case I__

Mat Weavers Mats

4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4

8Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â y

- Less mat weavers mean less mats.
- More mat weavers mean more mats.

This clearly indicates that there is direct relation.

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

4 : 8 :: 4 : y ________ (i)

__Case II__

Days Mats

4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4

8Â Â Â Â Â Â Â Â Â Â Â Â Â Â y

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

This clearly indicates that there is direct relation.

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

4 : 8 :: 4 : y ________ (ii)

By (i) and (ii)

4 : 8 :: 4 : y

4 : 8

4 x 4 x y = 8 x 8 x 4 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 16 mats)

## To Find

Mats woven by 8 mat-weavers in 8 days = ?

## Solution

__Method I__

Let suppose

Mats woven by 8 mat-weavers in 8 days = y

Mat Weavers Days Mats

4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4

8 Â Â Â Â Â Â Â Â Â Â Â Â Â Â 8Â Â Â Â Â Â Â Â Â Â Â Â Â Â y

- Relation between mat-weavers and mats is direct.
- Relation between days and mats is also direct.

So

4 : 8 :: 4 : y

4 : 8

4 x 4 x y = 8 x 8 x 4

16y = 256

y = 256/16

y = 16

**Mats woven by 8 mat-weavers in 8 days = 16 mats**

__Method II__

Mats woven by 4 mat-weavers in 4 days = 4 mats

Mats woven by 4 mat-weavers in 1 day = 4/4 mat

Mats woven by 4 mat-weavers in 1 day = 1 mat

Mats woven by 1 mat-weaver in 1 day = 1/4 mat

Mats woven by 1 mat-weaver in 8 days = 8/4 mats

Mats woven by 1 mat-weaver in 8 days = 2 mats

Mats woven by 8 mat-weavers in 8 days = (2 x 8) mats

Mats woven by 8 mat-weavers in 8 days = 16 mats

**Mats woven by 8 mat-weavers in 8 days = 16 mats**

## Conclusion

4 mat-weavers can weave 4 mats in 4 days. At the same rate 16 mats would be woven by 8 mat-weavers in 8 days.