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A cistern has a leak which would empty it in 8 hrs. A tap is turned on which admits 6 litres a minute into the cistern, and it is now emptied in 12 hours. How many litres does the cistern hold?

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A cistern has a leak which would empty it in 8 hrs. A tap is turned on which admits 6 litres a minute into the cistern, and it is now emptied in 12 hours. How many litres does the cistern hold?
1). 8640
2). 8740
3). 8840
4). 8940


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1 answers

4 vote
Answered by on | Votes 4 |

Let the volume of cistern be v.

In one minute a tap fills 6 litres.

In 1 hour it will fill 6 × 60 litres = 360 litres

To fill v litres number of hours it will take = v/360

Leak in the cistern empties it in 8 hours.

In 12 hours cistern is empty if tap I opened

∴ 1/8 – 1/(v/360) = 1/12

⇒ 360/v = 1/24

⇒ v = 360 × 24 = 8640 litres

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