Latest CAT Aptitude Question SOLUTION: A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min,but a third pipe can empty it in 6 min. the first two pipes are kept open for 5 min in the beginning and

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(#M40034672) CAT Numerical Ability question pipes and cisterns Keep an EYE

A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min,but a third pipe can empty it in 6 min. the first two pipes are kept open for 5 min in the beginning and then the third pipe is also opened.in what time is the cistern emptied

Asked In CAT ramakrishna (10 years ago)

Solved Ann Theressa Read Solution (6)

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Read Solution (6) :

Ann Theressa  (10 years ago)

45 min

In 1 min
1st pipe fills =1/12
2nd pipe fills =1/15

In 1st 5 min
fraction of cistern filled = 5/12 + 5/15
=(25+20)/60
=45/60
=3/4

Since the 3 pipes are opened after 5 mins,
fraction emptied in 1 min = 1/6 - (1/12 + 1/15)
=(10-5+4)/60
=1/60

===>60 min to empty fully filled cistern
Since the cistern is 3/4 filled

Time taken to empty = 60*3/4
=45 minutes

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sravani  (9 years ago)

5(1/12 + 1/15 )=45/60
remaining work there for is 1 - 45/60=15/60
let the time taken be x hrs.
x(1/6 - 1/12 + 1/15 )=3/4
x=45 mins
so it takes 45 mins to empty the tank

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sravani  (9 years ago)

the filled part is 5(1/12 + 1/15)=3/4
let X be time taken to empty the tank..
so,
X(1/6)=3/4
X=9/2 mins...
X=4mins 30 secs...

Is this solution Helpfull? Yes | No (1)  

Naveen Chaudhary  (8 years ago)

let the tank be of 60 L (Lcm of 14 & 15)
1st pipe will fill=60/12=5 L per min
& 2nd pipe will fill=60/15=4 L per min
1+2 pipe will fill=(5+4) 9 L per min
since 1 & 2 are opened for 1st 5 min ,
then tank filled=9*5=45 L

3rd can empty=60/6=10 L per min

when third pipe is opened

1+2+3 pipe will fill=5+4-10= -1 L per min
that means will emty 1 L per min.

so 45/1=45 min will be taken to emty the tank

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aman Kumar  (8 years ago)

A(fill)->12min
b(fill)->15min
c(empty)->6min
lcm(15,10,6)=60unit ->total work
A->60/12->5unit/min,B->60/15->4unit/min,C->60/6->10unit/min
A+B=9unit /min in 5min=45unit water fill
A+B+c=5+4-10=-1unit/min
so,empty in 45 min

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Sidharth Soren  (7 years ago)

when all 3 pipes will be open it will take time = 45min
Soln:
time by first pipe= 12min
time by 2nd pipe=15min
time taken by 3rd pipe to empty=6min
work done by 1st pipe(per min ) = 1/12
work done by 2nd pipe(per min)= 1/15
work done by 3rd pipe(per min)= 1/6
work done by 1st&2nd pipes in min=(1/15+1/12)
= 3/20
work done by them in 5 min= 3/4
when all pipes are open cistern drained in min=1/60
time to drain 3/4 of cistern =45min

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