Aptitude - Pipes and Cistern - Discussion

1. 

Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

[A].
5
11
[B].
6
11
[C].
7
11
[D].
8
11

Answer: Option B

Explanation:

Part filled by (A + B + C) in 3 minutes = 3 1 + 1 + 1 = 3 x 11 = 11 .
30 20 10 60 20

Part filled by C in 3 minutes = 3 .
10

Required ratio = 3 x 20 = 6 .
10 11 11


Angel said: (Sep 26, 2010)  
How 3/10 came ? Please explain it in detail.

PRAKASH KUMAR said: (Oct 14, 2010)  
Is there is any shortcut methods in understanding the pipes and cisterns problems?

Yukta said: (Jan 5, 2011)  
R is belongs to C.The ratio of the solution is obtained from dat.

Akshay said: (Jan 7, 2011)  
@Angle

When c works for 1 min its work done in 1 min = 1/10

so when it works for 3 min its contribution = 3/10

Rakesh K said: (Jan 8, 2011)  
Is there any shortcuts to find pipes problems?

Dine said: (Jan 12, 2011)  
They asking after 3 min
so they given as a b c proportional to p q r .
so r is c for 3 min it 3/10.

Lalli said: (Jan 19, 2011)  
How 3/10*20/11=6/11 came? please explain.

Ajay said: (Feb 9, 2011)  
Part filled by C in 3 minutes = 3/10
Part filled by (A + B + C) in 3 minutes = 3 ( 1/30+ 1/20 +1/10)= 3*11/60 = 11/20


Required ratio = chemical soluttion R in tank/ total chemical solution in tank
i.e. 3/10/11/20

= 3*20/10*11
= 60/110
= 6/11

Aarti said: (Mar 22, 2011)  
How 11/60 came? where is this 11 came from ?

Sumanth Gowda said: (Jun 24, 2011)  
Hey guys listen properly.

A part filled by 3 min
for a=1/30,b=1/20,c=1/20
first u add this tree and multiply by 3 min k then u'l get 11/20
discharge chemical solutions P,Q and R respectively its equal to A,Band C
observe carefully P=A,Q=B,R=C;
proportion of the solution R in the liquid in the tank after 3 minutes where 3min s nothing but 3(C).....3(1/10) ie 3/10

Now u got ans.

Vengatesh said: (Jul 2, 2011)  
How is 11/60? from where this 11 came from? please explain.

Srinivasan said: (Aug 6, 2011)  
1/30 + 1/20 + 1/10 = {(2*1)+(3*1)+(6*1)}/60
= 11/60
do L.C.m Now add this, we'ii got wht u wnt...
It's simple........

Aks said: (Sep 26, 2011)  
How 3/10 came? means 10 came from where?

M@n> said: (Sep 30, 2011)  
Why should we multiply 3 with a b and c i.e 3*(1/30+1/20+1/10) ?

Lalitha said: (Nov 30, 2011)  
If 1/30,1/20,1/10 added we get 3/60 how 11/60 ?

Rajthilak said: (Dec 14, 2011)  
@Sumanth Gowda thanks I understand now.

Sashank Singh said: (Jan 6, 2012)  
A, B and C can fill a tank in 6 hrs. After 2 hrs C is stopped. Then A and B together fill the tank in 7 hrs.

How much C will take individully take to fill the tank?

Deepi said: (Feb 5, 2012)  
Hi Sashank Singh

Let me explain in detail.

(A,B and C)Three pipes work together 2 hours from that completed work is
(1/6)*2=1/3
The remaining work is 2/3.
This 2/3 work is done by A and B alone 7hrs.
That is
2/3 =7hrs
1 =? =>7*3/2=21/2hrs
A,B&c=6hrs
A&B=21/2hrs
lets take A,B&C total work time is X and A,B work time is Yhrs.
To find A alone use the formula as (X*Y)/(Y-X)
(6*21/2)/(21/2-6)=14

Sailumukund said: (Apr 8, 2012)  
Any more short cuts in commercial mathematics.

Shakthi said: (Jul 25, 2012)  
Hi,

Please any one check whether my solution is right?

'A' fills tank =30 mins.
'B' fills tank =20 mins.
'C'fills tank =10 mins.

So if we find the LCM for this means we'll assume it as our tanks capacity,

Here its LCM is 60
The tanks capacity is 60 litres

A' fills d tank= 2 lit/min
B' fills d tank=3 lit / min
C' fills d tank=6 lit / min

(A+B+C)'s fill d tank = 11 lit/min

A , B , C respectively discharge P,Q,R respectively

So C it self discharge 6/11 lit

Sandhiya said: (Aug 21, 2012)  
Pipe A fills the tank in 30 min
in one min pipe A fills 1/30 of the tank
pipe B fills the tank in 20 min
in one min pipe B fills 1/20 of the tank
pipe C fills the tank in 10 min
in one min pipe C fills 1/10 of the tank
part of the tank filled when all the three pipes are opened for one min is {(1/30)+(1/20)+(1/10)}=11/60
the part of the tank filled when all three pipes are opened for
three min is =3*(11/60)=33/60=11/20
now the chemical solution R present after 3 min=3*(part of the tank filled by C for one min)
=3*1/10=3/10
propotion of sol R in the tank after 3min=(chemical soln r in the tank after 3 min)/(total chemical soln in the tank)
=(3/10)/(11/20)=(3*20)/(11*10)=60/110=6/11
hence the ans is 6/11

Kiran said: (Oct 12, 2012)  
@Lalitha

= 1/30+1/20+1/10
So L.C.M of 30,20,10=60
Then 1/30+1/20+1/10=2+3+6/60
=11/60
ok

Shrikant said: (Jan 11, 2014)  
Don't make this type of questions complicated.

I am giving you simple solution which I gives in my class for this type of questions.

Just take LCM of all given values.

30, 20, 10 = 60 (LCM).

Assume that capacity of tank is 60 liters.

Now find the capacity of each pipe of filling the tank by.

* Total capacity of tank in liters / time taken by specific pipe.

1) Pipe A capacity 60 / 30 = 2 liters every min(solution P).
2) Pipe B capacity 60 / 20 = 3 liters every min(solution Q).
3) Pipe c capacity 60 / 10 = 6 liters every min(solution R).

Clearly if all works together than the capacity is 2+3+6 = 11.

Liters per minute. Now out of 11 pipe c (solution R) have 6 liters so in all solution in 1 minute solution are share should 6/11 (don't need to multiply by 3 minutes because the ratio will remain same for 1, 2, 3, 4. Any number of minutes) its very easy to solve any problem of pipe and cistern using this method, it looks lengthy in reading but if you practice I assure you, everyone of you will solve this type of questions in few seconds.

Niranjan Kumar said: (Jul 11, 2014)  
A - 30 min.
B - 20 min.
C - 10 min.
Now take LCM (30,20,10) = 60.

So,
A - 60/30 = 2 LTR.
B - 3LTR.
C - 6 LTR.

So TOTAL 2+3+6 = 11 LTR.
So proportion of C is 6/11.

So Simple.

Ankit Jhunjhunwala said: (Sep 4, 2014)  
At any time proportion of solution R is same with respect to other two solution,

In 1 minute A will drop =1/30.
" " "" " " B will drop =1/20.
" " " " " C will drop =1/10.

Multiplying 60 to each one,
A:B:C = 2:3:6.
Since solution R corresponds to C we have = 6/(6+3+2) = 6/11.

Shubha Sahu said: (Sep 7, 2014)  
Please tell me if there is any shortcut to solve this questions?

G.Nandhini said: (Jan 17, 2015)  
Proportion of are in the tank = Amount of are filled by Tap C in 3 min/Total amount of P, Q, are filled by Taps A, B, C for 3 mins.

Sachin said: (Jan 22, 2015)  
Why divided 3/10 by 11/60?

Anand said: (Jun 19, 2015)  
Percentage filled by A in 3 minute = 100x3/30.....1.

Percentage filled by B in 3 minute = 100x3/20.....2.

Percentage filled by C in 3 minute = 100x3/10.....3.

= 3/(1+2).

Xyz said: (Nov 5, 2015)  
Please give some simple explanation. Please tell me how to calculate LCM? I forgot it.

Sujohn Rayamajhi said: (Jan 17, 2016)  
Why C's filling is counted twice? Once in total and then individually.

Drishti Anand said: (Apr 11, 2016)  
Why they took the reciprocal of 11/20 in final step?

Archisha said: (Apr 12, 2016)  
@Drishti Anand.

In the end, we are doing (3/10) / (11/20).
Which is equal to (3/10) * (20/11)
That's why we take it in reciprocal.

Sadia said: (Apr 24, 2016)  
Can anybody share the simple method for this question?

Nishant said: (Apr 30, 2016)  
Why we reciprocal 11/20?

Please tell the answer.

Bindu said: (May 19, 2016)  
Is there any easy trick to solve this problem, Plese tell me.

Roja said: (Jul 5, 2016)  
11/60 is the LCM.

Raji said: (Aug 9, 2016)  
You are right @Shakthi.

Vinod said: (Aug 13, 2016)  
Please, anyone of you tell me How 11/20 is reciprocated?

Sravanthi said: (Sep 17, 2016)  
Is it liters or minutes for a, b, c can you explain the question?

JISHNU said: (Nov 13, 2016)  
Regardless of the minutes the ratio will always the same,

i.e, the ratio is [1/10] / [(1/30) + (1/20) + (1/10)] = (1/10)/(11/60) = 6/11.

Hrishi said: (Nov 23, 2016)  
Great & better solution @Niranjankumar.

Doug said: (Jan 2, 2017)  
Just to make it easier for you guys let me show you my trick to solve this particular question.

So, first we have to find out the total capacity of the tank so for that we have to find out the lcm of the above 3 no's.

i.e 30/20/10 so lcm would be 60 and this 60 is the capacity of the tank.
Now let us find out the speed at which the tank will be filled so just divide the total capacity with the given time.
i.e : 60/30, 60/20, 60/10

Now we have the the speed at which this tank will be filled i.e 2lt/min, 3lt/min and 6lt/min.
If a pipe can fill 2 lt of chemical in 1 min so how much will be the amount of chemical after 3 min. i.e 6lt similarly for b it would be 9lt and for c it will be 18lt and we have the calculate the ratio of chemical l after 3 min.

So the ratio can be calculated as shown below:

18(amount of chemical after 3min)/18 + 9 ++6 = 18/33ie 6/11 (solution).

Zara said: (Apr 17, 2017)  
The section is the great help for me. Thanks.

K Ravikumar said: (May 25, 2017)  
A pipe can fill 10% in three minutes that is 100÷3 * 100=10% b can fill 15% in three minutes 100/20=5.

5*3minutes =15%.
Similarly, C can fill in three minutes 30% so in three minutes entire work is 55% so C proportion is30÷55 = 6÷11.

Jothi said: (Jun 15, 2017)  
1 =? =>7*3/2=21/2hrs.

Please explain in detail.

Moon said: (Aug 10, 2017)  
Part filled by (A + B + C) in 3 minutes = 3 = 1 + 1 + 1.

3 x 11 = 11.

30 20 10 60 20

Part filled by C in 3 minutes = 3.
10
Required ratio = 3x20= 6.
10 11 11

Mohsin said: (Aug 28, 2017)  
Why made reciprocal of 11/20? please explain it.

Prabhas said: (Oct 28, 2017)  
3/10*20/11=6/11?

Plz explain.

MrunalMehta said: (Jan 19, 2018)  
@Mohsin & @Prabhas.


The part filled by C in 3 mins is 3/10 and part filled by all three combined together is 11/20. To find the proportion of solution are we have to divide 3/10 by 11/20, thus multiplied by 20/11*.

If we divide a number say 25 by 5 we have 2 options.

I) 25/5 i.e- 5 or.
II) 25 x INVERSE OF 5 (I. E- 1/5) = 25x 1/5.
Both are one and the same. Hope this clears.

Bibhuti Bhusan Swain said: (Feb 28, 2018)  
@Lalli.

When 1/30+1/20+1/10 add up they give 11/60.

Divya.chippada said: (Mar 27, 2018)  
Part filled by A in one min is given by=1/30 min.
Part filled by B in one min is given by=1/20 min.
Part filled by C in one min is given by=1/10 min.

Now, total (A+B+C)filled in 1 min is given as (1/30+1/20+1/10) by taking lcm and we get 11/20
then in the qn they said after 3 min proportion of R ....clearly we are knowing that (A=p),(B=Q),(C=R).

So we should consider the value of c.
To calculate the proportion of R after 3 min,
Now part filled by C in 3 min is 3x(1/10)=3/10,
the proportion of R=total filled /c filled,
= (3/10)x(20/11),
= 6/11.

Vignes R said: (Apr 15, 2018)  
If pipe c is empty the tank. Put negative sign Why use + sign?

Shailesh Vishwakarma said: (Jun 9, 2018)  
A = 30min fill 100%.
B = 20min fill 100%.
C = 10min fill 100%.

if 3 min filling done all together then,
A =3min fill 10%,
B =3min fill 15%,
C =3min fill 30%.

P =10%,
Q = 15%,
R = 30%.

Total = 55% total tank filled.

Proportion of soln R in total liquid,
=R/Total,
=30/55,
=6/11.

Anitha said: (Aug 19, 2018)  
C spend max time 10 minutes.
So, 3/10 minutes.
(3/10)*(20/11).
6/11.

Amit Ravanak said: (Oct 11, 2018)  
How 6/11?

Please explain in detail.

Guruprasad R said: (Feb 9, 2019)  
How 11/60? please explain.

Rohit said: (Aug 11, 2019)  
LCM of 20,30 and 60 are but ratio 3,2 and 1 and their lcm is 6 which is diveded as by 2,3,6 respectively. Now sum is 11 and after 3 minutes q {3} 3+3 =6 /11

Abey said: (Sep 8, 2019)  
How 3/10? Please explain.

Satya said: (Dec 27, 2019)  
Why made reciprocal of 11/20? Please explain it.

Deepanshu Sharma said: (Apr 8, 2020)  
@Satya.

Initially, we calculate as per pipe and for total, we need to do reciprocal.

MOHAMMED KHAN SABBIR said: (Sep 17, 2020)  
Solution:

A = 30.
B = 20.
C = 10.
LCM = 60.
A:B:C = 2:3:6.

REQUIRED TIME FOR (A+B+C) = 60/11,
REQUIRED TIME FOR C = 60/6 = 10,
RATIO = (6O/11)/10 = 6/11.

Mruthyunjaya Bm said: (Oct 5, 2020)  
Filled by C in 3 minutes = 3/10.
Filled by (A + B + C) in 3 minutes = 3 ( 1/30+ 1/20 +1/10)= 3*11/60 = 11/20.
As they told A B C proportional to P Q R (R=C).
Required ratio = chemical solution R in tank/ total chemical solution in tank.
i.e. (3/10)/(11/20),
=(3/10)*(20/11),
= (3*20)/(10*11),
= 60/110,
= 6/11.

Aman Kumar said: (Oct 12, 2020)  
According to me,

30, 20, 10 LCM 60 means per unit of each pipe is;

2, 3, 6 total unit = 11.

We can write this way also 60\11 *3\10 = 6\11.

Nandeesh said: (Jul 24, 2021)  
3/30 + 3/20 + 3/10.
(6+9+18)/60 = 33/60 = 11/20,
(3/10)/11/20 = (3/10*20/11) = 6/11.

Saloni said: (Aug 15, 2021)  
Why do we reciprocal 11/20? Explain please.

Hritik said: (Aug 31, 2021)  
How 20/11 came? Explain please.

Subu said: (Sep 13, 2022)  
Lcm = 60 .it means total tank capacity is 60 lit.
A done in one min = 60/30= 2lit,
B done in one min = 60/ 20= 3 lit,
C done in one min = 60/ 10 = 6 lit,
So Total lit in one min = 11 lit,
So Total lit in three mints = 11 * 3 = 33 lit,
C done in three min = 6 * 3 = 18.
C' share is after three mints = 18/33 = 6/11 ans.

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