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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?

  • 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

  1. Pumps
  2. Hours
  3. 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.

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