- 39 persons can repair a road in 12 days working 5 hours a day.
- The days required to complete the work by 30 persons working 6 hours a day can be figure out in this way.
Explanation
Three given entities here are
- Person
- Hours
- Days
To determine the relation here, let suppose; The days required to complete the work by 30 persons working 6 hours a day = y
Case I
Person Days
39 12
30 y
- More persons mean less days to get the job done.
- Less persons mean more days to complete the job.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
39 : 30 :: y : 12 ________ (i)
Case II
Hours Days
5 12
6 y
- Less hours mean more days.
- More hours mean less days.
This clearly indicates that there is also inverse relation.
Direct/Indirect relation tells how the equation will be written.
5 : 6 :: y : 12 ________ (ii)
By (i) and (ii)
39 : 30 :: y : 12
5 : 6
39 x 5 x 12 = 30 x 6 x y ________ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 13)
To Find
The days required to complete the work by 30 persons working 6 hours a day = ?
Solution
Method I
Let suppose
The days required to complete the work by 30 persons working 6 hours a day = y
Person Hours Days
39 5 12
30 6 y
- Relation between persons and days is inverse.
- Relation between hours and days is also inverse so;
39 : 30 :: y : 12
5 : 6
39 x 5 x 12 = 30 x 6 x y
2340 = 180y
2340/180 = y
13 = y
y = 13 days
The days required to complete the work by 30 persons working 6 hours a day = 13 days answer
Method II
The days required to complete the work by 39 persons working 5 hours a day = 12 days
The days required to complete the work by 39 persons working 1 hours a day = (12 x 5) days
The days required to complete the work by 1 person working 1 hours a day = (12 x 5 x 39) days
The days required to complete the work by 1 persons working 6 hours a day = 2340/6 days
The days required to complete the work by 1 persons working 6 hours a day = 390 days
The days required to complete the work by 30 persons working 6 hours a day = 390/30 days
The days required to complete the work by 30 persons working 6 hours a day = 13 days
The days required to complete the work by 30 persons working 6 hours a day = 13 days answer
Conclusion
39 persons can repair a road in 12 days working 5 hours a day. In 13 days, 30 persons working 6 hours a day can complete the work.
