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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

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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