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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

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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