- 3 pumps working 8 hours a day can empty a tank in 2 days.

- Hours that 4 pumps require to empty the tank in one day can be figure out in this way.

## Explanation

Three given entities here are

- Pump
- Days
- Hours

To determine the relation here, let suppose; Hours that 4 pumps require to empty the tank in one day = y

__Case I__

Pump Hours

3 8

4 y

- Lesser pumps mean more time that would require more hours.
- More pumps mean less time.

This clearly indicates that there is inverse relation.

Direct/Indirect relation tells how the equation will be written.

3 : 4 :: y : 8 ________ (i)

__Case II__

Days Hours

2 8

1 y

- More days mean less hours.
- Less days mean more hours.

This clearly indicates that there is also inverse relation.

Direct/Indirect relation tells how the equation will be written.

2 : 1 :: y : 8 ________ (ii)

By (i) and (ii)

3 : 4 :: y : 8

2 : 1

3 x 2 x 8 = 4 x 1 x y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 12 hours)

## To Find

Hours that 4 pumps require to empty the tank in one day = ?

## Solution

__Method I__

Let suppose

Hours that 4 pumps require to empty the tank in one day = y

Pump Days Hours

3 2 8

4 1 y

- Relation between pump and hours is inverse.
- Relation between days and hours is also inverse so;

3 : 4 :: y : 8

2 : 1

3 x 2 x 8 = 4 x 1 x y

48 = 4y

4y = 48

y = 48/4

y = 12 hours

**Hours that 4 pumps require to empty the tank in one day**** = 12 hours answer**

__Method II__

Hours that 3 pumps require to empty the tank in 2 days** = **8 hours

Hours that 3 pumps require to empty the tank in 1 day** = **(8 x 2) hours

Hours that 1 pump require to empty the tank in 1 day** = **(8 x 2 x 3) hours

Hours that 1 pump require to empty the tank in 1 day** = **48 hours

Hours that 4 pump require to empty the tank in 1 day** = **48/4 hours

Hours that 4 pump require to empty the tank in 1 day** = **12 hours

**Hours that 4 pumps require to empty the tank in one day**** = 12 hours answer**

### Conclusion

3 pumps working 8 hours a day can empty a tank in 2 days. 12 hours a day must 4 pumps work to empty the tank in one day.