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If 3 Men or 6 Boys can Do a Piece of Work in 10 Days Working 7 Hours a Day; How Many Days will It Take to Complete a Piece of Work Twice as Large with 6 Men and 2 Boys Working Together for 8 Hours a Day?

  • If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day.
  • Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large can be figure out in this way.

Explanation

Three given entities here are

  • Boys
  • Hours
  • Days

To determine the relation here, let suppose; days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y

Case I

As

3 men = 6 boys

1 man = 2 boys

6 men = 12 boys

6 men and 2 boys = 14 boys

Boys          Days

6                 10

14                y

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

This clearly indicates that there is inverse relation.

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

14 : 6  ::  10 : y ________ (i)

Case II

Hours         Days

7                 10

8                 y

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

This clearly indicates that there is inverse relation.

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

8 : 7  ::  10 : y ________ (ii)

By (i) and (ii)

14 : 6  ::  10 : y

8 : 7

14 x 8 x y = 6 x 7 x 10 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 7.5 days)

To Find

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = ?

Solution

Method I

Let suppose

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = y

Boys          Hours         Days

6                 7                 10

14             8                y

  • Relation between boys and days is inverse.
  • Relation between hours and days is also inverse.

So

14 : 6  ::  10 : y

8 : 7

14 x 8 x y = 6 x 7 x 10

112y = 420

y = 420/112

y = 3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work = 3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days

Method II

As

3 men = 6 boys

1 man = 2 boys

6 men = 12 boys

6 men and 2 boys = 14 boys

Days required by 6 boys working for 7 hours a day to complete a piece of work = 10 days

Days required by 6 boys working for 1 hour a day to complete a piece of work = (10 x 7) days

Days required by 6 boys working for 1 hour a day to complete a piece of work = 70 days

Days required by 1 boy working for 1 hour a day to complete a piece of work = (70 x 6) days

Days required by 1 boy working for 1 hour a day to complete a piece of work = 420 days

Days required by 1 boy working for 8 hours a day to complete a piece of work = 420/8 days

Days required by 1 boy working for 8 hours a day to complete a piece of work = 52.5 days

Days required by 14 boys working for 8 hours a day to complete a piece of work = 52.5/14 days

Days required by 14 boys working for 8 hours a day to complete a piece of work = 3.75 days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = (3.75 x 2) days

Days required by 6 men and 2 boys working together for 8 hours a day to complete a piece of work twice as large = 7.5 days

Conclusion

If 3 men or 6 boys can do a piece of work in 10 days working 7 hours a day; 7.5 days it will take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day.

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