- 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.