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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

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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