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4 Mat-Weavers can Weave 4 Mats in 4 Days. At the Same Rate How Many Mats would be Woven by 8 Mat-Weavers in 8 Days?

  • 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

4                 4

8                 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

4                 4

8                 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

4                 4                 4

8                8                 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.

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