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If 15 Men Working 9 Hours a Day can Reap a Field in 16 Days, in How Many Days will 18 Men Reap the Field, Working 8 Hours a Day?

  • If 15 men working 9 hours a day can reap a field in 16 days.
  • Then the required days in which 18 men reap the field, working 8 hours a day can be figure out in this way.

Explanation

Three given entities here are

  1. Men
  2. Hours
  3. Days

To determine the relation here, let suppose; days required by the 18 men to reap the field, working 8 hours a day = y

Case I

Men           Days

15               16

18               y

  • Less men means more days required to finish a particular job.
  • More men means less days are required to get the job done.

This clearly indicates that there is inverse relation.

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

18 : 15  ::  16 : y ________ (i)

Case II

Hours                  Days

9                 16

8                 y

  • More hours means less days.
  • Less days means more hours would be required to get the job done.

This clearly indicates that there is inverse relation.

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

8 : 9  ::  16 : y ________ (ii)

By (i) and (ii)

18 : 15 :: 16 : y

  8 : 9

15 x 9 x 16 = 18 x 8 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 49)

To Find

Days required by the 18 men to reap the field, working 8 hours a day = ?

Solution

Method I

Let suppose

Days required by the 18 men to reap the field, working 8 hours a day = y

Men           Hours         Days

15               9                 16

18               8                 y

Relation between men and days & hours and days is inverse so;

18 : 15 :: 16 : y

  8 : 9

15 x 9 x 16 = 18 x 8 x y

2160 = 144y

y = 2160/144

y = 15 days

Days required by the18 men to reap the field, working 8 hours a day = 15 days answer

Method II

Days required by 15 men, working 9 hours a day = 16 days

Days required by 15 men, working 1 hour a day = 16 x 9 days

Days required by 15 men, working 1 hour a day = 144 days

Days required by 1 man, working 1 hour a day = 144 x 15 days

Days required by 1 man, working 1 hour a day = 2160 days

Days required by 18 men, working 1 hour a day = 2160/18 days

Days required by 18 men, working 1 hour a day = 120 days

Days required by 18 men, working 8 hours a day = 120/8 days

Days required by 18 men, working 8 hours a day = 15 days

Days required by the18 men to reap the field, working 8 hours a day = 15 days answer

Conclusion

If 15 men working 9 hours a day can reap a field in 16 days, in 15 days 18 men will reap the field, working 8 hours a day.

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