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If 18 Pumps can Raise 2170 Tonnes of Water in 10 Days Working 7 Hours a Day then in How Many Days will 16 Pumps Raise 1736 Tonnes of Water Working 9 Hours a Day?

  • 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

  1. Pumps
  2. Tonnes
  3. Hours
  4. 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.

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