- 49 pumps can empty a reservoir in 6.5 days working 8 hours a day.
- Days required to empty a reservoir if 196 pumps are used for 5 hours each day can be figure out in this way.
Explanation
Three given entities here are
- Pumps
- Hours
- Days
To determine the relation here, let suppose; Days required to empty a reservoir if 196 pumps are used for 5 hours each day = y
Case I
Pumps Days
49 6.5
196 y
- Less pumps mean more days.
- More pumps would require less days.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
49 : 196 :: y : 6.5 ________ (i)
Case II
Hours Days
8 6.5
5 y
- More hours mean less days.
- Less hours mean more days.
This clearly indicates that there is also inverse relation.
Direct/Indirect relation tells how the equation will be written.
8 : 5 :: y : 6.5 ________ (ii)
By (i) and (ii)
49 : 196 :: y : 6.5
8 : 5
196 x 5 x y = 49 x 8 x 6.5 ________ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 2.6)
To Find
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = ?
Solution
Method I
Let suppose
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = y
Pumps Hours Days
49 8 6.5
196 5 y
- Relation between pumps and days is inverse.
- Relation between hours and days is also inverse.
49 : 196 :: y : 6.5
8 : 5
196 x 5 x y = 49 x 8 x 6.5
980y = 2548
y = 2548/980
y = 2.6 days
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = 2.6 days answer
Method II
Days required to empty a reservoir if 49 pumps are used for 8 hours each day = 6.5 days
Days required to empty a reservoir if 49 pumps are used for 1 hour each day = (6.5 x 8) days
Days required to empty a reservoir if 49 pumps are used for 1 hour each day = 52 days
Days required to empty a reservoir if 1 pump is used for 1 hour each day = (52 x 49) days
Days required to empty a reservoir if 1 pump is used for 1 hour each day = 2548 days
Days required to empty a reservoir if 196 pumps are used for 1 hour each day = 2548/196 days
Days required to empty a reservoir if 196 pumps are used for 1 hour each day = 13 days
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = 13/5 days
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = 2.6 days
Days required to empty a reservoir if 196 pumps are used for 5 hours each day = 2.6 days answer
Conclusion
49 pumps can empty a reservoir in 6.5 days working 8 hours a day. If 196 pumps are used for 5 hours each day then the same work will be completed in 2.6 days.
