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

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Math Expert
Joined: 02 Sep 2009
Posts: 53006
A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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30 Jan 2019, 02:15
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:50) correct 33% (02:17) wrong based on 30 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

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Joined: 18 Aug 2017
Posts: 1838
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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30 Jan 2019, 03:01
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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Intern
Joined: 01 Feb 2018
Posts: 3
GMAT 1: 640 Q48 V30
A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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10 Feb 2019, 08:11
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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VP
Joined: 07 Dec 2014
Posts: 1156
A cistern has a leak which would empty it in 8 hours. A tap is turned  [#permalink]

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10 Feb 2019, 10:12
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
A cistern has a leak which would empty it in 8 hours. A tap is turned   [#permalink] 10 Feb 2019, 10:12
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# A cistern has a leak which would empty it in 8 hours. A tap is turned

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