- 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

18Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10

16Â Â Â Â Â Â Â Â Â Â Â Â 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

2170Â Â Â Â Â Â Â Â Â 10

1736Â Â Â Â Â Â Â Â Â 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

7Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10

9Â Â Â Â Â Â Â Â Â Â Â Â Â 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.