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A cistern has a leak which would empty it in 8 hours. A tap is turned

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A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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New post 30 Jan 2019, 03:15
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Difficulty:

  55% (hard)

Question Stats:

59% (02:52) correct 41% (02:21) wrong based on 49 sessions

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A cistern has a leak which would empty it in 8 hours. 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?

A. 7580
B. 7960
C. 8290
D. 8640
E. 8840
Spoiler: OA

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Re: A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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New post 30 Jan 2019, 04:01
1
Bunuel wrote:
A cistern has a leak which would empty it in 8 hours. 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?

A. 7580
B. 7960
C. 8290
D. 8640
E. 8840


initial rate =1/8
rate after 6 liters per min is been done = 1/12
so combined rate = 1/8-1/12 = 3-2/24 = 1/24
flow rate in hrs = 6* 60 = 360 ltrs per hr
so vol of cistern = 360 *24 = 8640 ltrs
IMO D
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A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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New post 10 Feb 2019, 09:11
1
let X be the rate of emptying.
total capacity of cistern = 8x
additional inflow at the rate of 360 l/hr = 12*360 = 4320
total volume emptied = 4320 + 8x

total volume emptied is also equal to 12x

so, 4320 + 8x = 12x
8x=8640

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A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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New post 10 Feb 2019, 11:12
1
Bunuel wrote:
A cistern has a leak which would empty it in 8 hours. 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?

A. 7580
B. 7960
C. 8290
D. 8640
E. 8840


if leak empties cistern in 8 hours,
in 12 hours it empties 1 1/2 cisterns
extra half cistern must come from tap:
6 lpm*60m*12h*2 halves=8640 litres cistern capacity
D
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A cistern has a leak which would empty it in 8 hours. A tap is turned   [#permalink] 10 Feb 2019, 11:12
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