12 Men Working 8 Hours Per Day Complete a Piece of Work in 18 Days. How Many Hours a Day Must 15 Men Work to Complete the Same Work in 12 Days?

  • 12 men working 8 hours per day complete a piece of work in 18 days.
  • Hours in a day for 15 men to complete the same work in 12 days can be figure out in this way.

Explanation

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Three given entities here are

  1. Men
  2. Days
  3. Hours

To determine the relation here, let suppose; Hours in a day for 15 men to complete the same work in 12 days = y

Case I

Men           Hours

12               8

15               y

  • Lesser men mean more hours in a day are required to finish the job.
  • More men mean less hours in a day to finish the given job.

This clearly indicates that there is inverse relation.

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

12 : 15  ::  y : 8 ________ (i)

Case II

Days           Hours

18               8

12               y

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

This clearly indicates that there is inverse relation.

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

18 : 12  ::  y : 8 ________ (ii)

By (i) and (ii)

12 : 15 :: y : 8

  18 : 12

12 x 18 x 8 = 15 x 12 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 9.6 hours)

To Find

Hours in a day for 15 men to complete the same work in 12 days = ?

Solution

Method I

Let suppose

Hours in a day for 15 men to complete the same work in 12 days = y

Men           Days           Hours

12               18               8

15               12               y

  • Relation between men and hours is inverse.
  • Relation between days and hours is also inverse so;

12 : 15 :: y : 8

  18 : 12

12 x 18 x 8 = 15 x 12 x y

1728 = 180y

1728/180 = y

y = 9.6

Hours in a day for 15 men to complete the same work in 12 days = 9.6 hours answer

Method II

Hours in 18 day for 12 men to complete the work = 8 hours

Hours in 18 days for 1 man to complete the work = (8 x 12) hours

 Hours in a day for 1 man to complete the work = (8 x 12 x 18) hours

Hours in 12 days for 1 man to complete the work = (8 x 12 x 18)/12 hours

Hours in 12 days for 15 men to complete the work = (8 x 12 x 18)/(12 x 15) hours

Hours in 12 days for 15 men to complete the work = 1728/180 hours

Hours in 12 days for 15 men to complete the work = 9.6 hours

Hours in a day for 15 men to complete the same work in 12 days = 9.6 hours answer

Conclusion

12 men working 8 hours per day complete a piece of work in 18 days. 9.6 hours a day must 15 men work to complete the same work in 12 days.

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