- If 18 pumps can raise 2170 tonnes of water in 10 days working 7 hours a day.
- Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day can be figure out in this way.
Explanation
Four given entities here are
- Pumps
- Tonnes
- Hours
- Days
To determine the relation here, let suppose; Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day = y
Case I
Pumps Days
18 10
16 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.
16 : 18 :: 10 : y ________ (i)
Case II
Tonnes Days
2170 10
1736 y
- 2170 tonnes require more days.
- 1736 tonnes require less days.
This clearly indicates that there is direct relation.
Direct/Indirect relation tells how the equation will be written.
2170 : 1736 :: 10 : y ________ (ii)
Case III
Hours Days
7 10
9 y
- Less hours mean more days.
- More hours mean less days.
This clearly indicates that there is inverse relation.
Direct/Indirect relation tells how the equation will be written.
9 : 7 :: 10 : y ________ (iii)
By (i), (ii) and (iii)
16 : 18 :: 10 : y
2170 : 1736
9 : 7
16 x 2170 x 9 x y = 18 x 10 x 1736 x 7 _ (A)
After simplifying equation (A), we can easily figure out the value of y (y = 7)
To Find
Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day = ?
Solution
Method I
Let suppose
Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day = y
Pumps Tonnes Hours Days
18 2170 7 10
16 1736 9 y
- Relation between pumps and days is inverse.
- Relation between tonnes and days is direct.
- Relation between hours and days is inverse.
So
16 : 18 :: 10 : y
2170 : 1736
9 : 7
16 x 2170 x 9 x y = 18 x 10 x 1736 x 7
312480y = 2187360
y = 2187360/312480
y = 7 days
Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day = 7 days answer
Method II
Days required by 18 pumps to raise 2170 tonnes of water working 7 hours a day = 10 days
Days required by 18 pumps to raise 2170 tonnes of water working 1 hour a day = (10 x 7) days
Days required by 18 pumps to raise 2170 tonnes of water working 1 hour a day = 70 days
Days required by 1 pump to raise 2170 tonnes of water working 1 hour a day = (70 x 18) days
Days required by 1 pump to raise 2170 tonnes of water working 1 hour a day = 1260 days
Days required by 1 pump to raise 1 ton of water working 1 hour a day = (1260/2170) days
Days required by 1 pump to raise 1 ton of water working 1 hour a day = 0.581 days
Days required by 1 pump to raise 1736 tonnes of water working 1 hour a day = (0.581 x 1736) days
Days required by 1 pump to raise 1736 tonnes of water working 1 hour a day = 1008 days
Days required by 1 pump to raise 1736 tonnes of water working 9 hours a day = (1008/9) days
Days required by 1 pump to raise 1736 tonnes of water working 9 hours a day = 112 days
Days required by 16 pump to raise 1736 tonnes of water working 9 hours a day = (112/16) days
Days required by 16 pump to raise 1736 tonnes of water working 9 hours a day = 7 days
Days required by 16 pumps to raise 1736 tonnes of water working 9 hours a day = 7 days answer
Conclusion
If 18 pumps can raise 2170 tonnes of water in 10 days working 7 hours a day then in 7 days 16 pumps raise 1736 tonnes of water working 9 hours a day.
