- 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
- Men and Women
- 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.
