- 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
- Men
- Hours
- 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.
