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
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