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39 Persons Can Repair a Road in 12 Days Working 5 Hours a Day. In How Many Days will 30 Persons Working 6 Hours a Day Complete the Work?

  • 39 persons can repair a road in 12 days working 5 hours a day.
  • The days required to complete the work by 30 persons working 6 hours a day can be figure out in this way.

Explanation

Three given entities here are

  1. Person
  2. Hours
  3. Days

To determine the relation here, let suppose; The days required to complete the work by 30 persons working 6 hours a day = y

Case I

Person        Days

39               12

30               y

  • More persons mean less days to get the job done.
  • Less persons mean more days to complete the job.

This clearly indicates that there is inverse relation.

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

39 : 30  ::  y : 12 ________ (i)

Case II

Hours         Days

5                 12

6                 y

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

This clearly indicates that there is also inverse relation.

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

5 : 6  ::  y : 12 ________ (ii)

By (i) and (ii)

39 : 30 :: y : 12

  5 : 6

39 x 5 x 12 = 30 x 6 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 13)

To Find

The days required to complete the work by 30 persons working 6 hours a day = ?

Solution

Method I

Let suppose

The days required to complete the work by 30 persons working 6 hours a day = y

Person        Hours         Days

39               5                 12

30               6                 y

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

39 : 30 :: y : 12

  5 : 6

39 x 5 x 12 = 30 x 6 x y

2340 = 180y

2340/180 = y

13 = y

y = 13 days

The days required to complete the work by 30 persons working 6 hours a day = 13 days answer

Method II

The days required to complete the work by 39 persons working 5 hours a day = 12 days

The days required to complete the work by 39 persons working 1 hours a day = (12 x 5) days

The days required to complete the work by 1 person working 1 hours a day = (12 x 5 x 39) days

The days required to complete the work by 1 persons working 6 hours a day = 2340/6 days

The days required to complete the work by 1 persons working 6 hours a day = 390 days

The days required to complete the work by 30 persons working 6 hours a day = 390/30 days

The days required to complete the work by 30 persons working 6 hours a day = 13 days

The days required to complete the work by 30 persons working 6 hours a day = 13 days answer

Conclusion

39 persons can repair a road in 12 days working 5 hours a day. In 13 days, 30 persons working 6 hours a day can complete the work.

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