20 Men Complete One-Third of a Piece of Work in 20 Days. How Many More Men should be Employed to Finish the Rest of Work in 25 More Days?

  • 20 men complete one-third of a piece of work in 20 days.
  • More men needed to finish the rest of work in 25 more days can be figure out in this way.

Explanation

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Three given entities here are

  1. Work
  2. Days
  3. Men

To determine the relation here, let suppose; Men needed to finish the rest of work in 25 more days = y

Case I

20 men complete work in 20 days = 1/3

Remaining work = 2/3

Work         Men

1/3              20

2/3             y

  • More work mean more men.
  • Less work mean less men.

This clearly indicates that there is direct relation.

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

1/3 : 2/3  ::  20 : y ________ (i)

Case II

Days           Men

20               20

25               y

  • More days mean less men.
  • Less days mean more men.

This clearly indicates that there is inverse relation.

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

25 : 20  ::  20 : y ________ (ii)

By (i) and (ii)

1/3 : 2/3  ::  20 : y

25 : 20

1/3 x 25 x y = 2/3 x 20 x 20 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 32) and more men = 32 – 20 = 12 men

To Find

More men needed to finish the rest of work in 25 more days = ?

Solution

Method I

Let suppose

Men needed to finish the rest of work in 25 more days = y

Work         Days          Men

1/3              20               20

2/3             25              y

  • Relation between work and men is direct.
  • Relation between days and men is inverse.

So

1/3 : 2/3  ::  20 : y

25 : 20

1/3 x 25 x y = 2/3 x 20 x 20

25y = 2 x 20 x 20

y = 2 x 4 x 4

y = 2 x 16

y = 32

Men needed to finish the rest of work in 25 more days = 32 men

More men needed to finish the rest of work in 25 more days = 32 – 20

More men needed to finish the rest of work in 25 more days = 12 men answer

Method II

Men needed to finish one-third of a work in 20 days = 20 men

Men needed to finish one-third of a work in 1 day = (20 x 20) men

Men needed to finish one-third of a work in 1 day = 400 men

Men needed to finish entire work in 1 day = (400 x 3) men

Men needed to finish entire work in 1 day = 1200 men

Men need to finish entire work in 25 days = 1200/25 men

Men needed to finish entire work in 25 days = 48 men

Men needed to finish 2/3 of work in 25 days = (48 x 2/3) men

Men needed to finish 2/3 of work in 25 days = 32 men

Men needed to finish the rest of work in 25 more days = 32 men

More men needed to finish the rest of work in 25 more days = 32 – 20

More men needed to finish the rest of work in 25 more days = 12 men answer

Conclusion

20 men complete one-third of a piece of work in 20 days. 12 more men should be employed to finish the rest of work in 25 more days.

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