If 5 Men or 9 Women can Do a Piece of Work in 19 Days then in How Many Days will 3 Men and 6 Women Do the Same Work?

  • If 5 men or 9 women can do a piece of work in 19 days.
  • The days required by 3 men and 6 women to do the same work can be figure out in this way.

Explanation

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Two given entities here are

  1. Men and Women
  2. Days

To determine the relation here, let suppose; The days required by 3 men and 6 women to do the same work = y

Case I

5 men = 9 women

1 man = 9/5 women

3 men = 27/5 women

This clearly indicates that 9 women do the same work as 5 men and 27/5 women do the same wok as 3 men.

When units of given quantities are different we need to change them accordingly.

3 men and 6 women = (27/5 + 6) women

3 men and 6 women = (27 + 30)/5 women

3 men and 6 women = 57/5 women

Case II

Women      Days

9                 19

57/5           y

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

This clearly indicates that there is inverse relation.

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

9 : 57/5  ::  y : 19 ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 15)

To Find

The days required by 3 men and 6 women to do the same work = ?

Solution

Method I

Let suppose

The days required by 3 men and 6 women to do the same work = y

Women      Days

9                 19

57/5           y

  • Relation between women and days is inverse so;

9 : 57/5  ::  y : 19

57/5 x y = 9 x 19

57y/5 = 171

57y = 171 x 5

57y = 855

y = 855/57

y = 15 days

The days required by 3 men and 6 women to do the same work = 15 days answer

Method II

5 men = 9 women

1 man = 9/5 women

3 men = 27/5 women

And

3 men and 6 women = (27/5 + 6) women

3 men and 6 women = (27 + 30)/5 women

3 men and 6 women = 57/5 women

The days required by 9 women to do the same work = 19 days

The days required by 1 woman to do the same work = (19 x 9) days

The days required by 1 woman to do the same work = 171 days

The days required by 57/5 women to do the same work = (171 x 5)/57 days

The days required by 57/5 women to do the same work = 15 days

The days required by 3 men and 6 women to do the same work = 15 days answer

Conclusion

If 5 men or 9 women can do a piece of work in 19 days, then 15 days would be required by 3 men and 6 women do the same work.

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