Aptitude - Pipes and Cistern - Discussion

10. 

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

[A]. 10 min. 20 sec.
[B]. 11 min. 45 sec.
[C]. 12 min. 30 sec.
[D]. 14 min. 40 sec.

Answer: Option D

Explanation:

Part filled in 4 minutes = 4 1 + 1 = 7 .
15 20 15

Remaining part = 1 - 7 = 8 .
15 15

Part filled by B in 1 minute = 1
20

1 : 8 :: 1 : x
20 15

x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec.
15 3

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.


Kalpna said: (Oct 14, 2010)  
Another method could be : 4/15+x/20=1

x=44/3 i.e 14 min 40 sec.

4/15 is the part filled by A in 4 mins

and x is the total time taken to fill the tank by B.

Priya P. said: (Dec 2, 2010)  
@ kalpna.

Thanks. Really less time consuming.

Santhu said: (Dec 15, 2010)  
Hi kalpana how u solve this x value

4/15+x/20=1

from above equation x val is = 46/3 its not 44/3....

Naveen said: (Dec 15, 2010)  
Hi santhu.

Its 44/3 only.

Satyajit said: (Mar 12, 2011)  
@thnx kalpna

Talha said: (Sep 4, 2011)  
How is 44/3 = 14 min 40 sec ?

Anjali said: (Sep 17, 2011)  
Hi Kalpna,

How you write 44/3 = 14 min 40 sec ?

Sundar said: (Sep 17, 2011)  
@Talha

It is simple yaar.

44/3 minutes =

= 14(2/3) mins

= 14 min 40 seconds ( 2/3 x 60 = 40 seconds)

= 14 min 40 seconds.

Preeti said: (Dec 6, 2011)  
Another method could be : (1/15 + 1/20)*4 + (1/20)*x-4 = 1

7/15 + (X-4)/20 = 1

Hence x=44/3.

= 14(2/3) mins

= 14 min 40 seconds ( 2/3 x 60 = 40 seconds)

Here 7/15 is the part filled by (A + B) in 4 mins.

and (x-4) is the total time taken to fill the tank by B alone.

Here 1 means show full tank.

Mahi said: (Jul 29, 2012)  
Thanks kalapana your solution is time consuming.

Pavi said: (Sep 16, 2012)  
Thank you sundar.

Sudan said: (Jun 6, 2013)  
I am weak in Maths. Please can anyone help me how to convert 44/3 into 14(2/3) ?

Nikhil said: (Jul 2, 2013)  
@Sudan.

Change fraction into mixed fraction.

Eg: 7/2 can be written in form on 3(1/2).

Divide numerator with denominator and whatever remainder you got write it in bracket.

Eg: a/b can be written as c(remainder/b).

Teju said: (Dec 11, 2013)  
Can anybody explain 1/20:8/15::1:x?

Deepak Verma said: (Jul 20, 2014)  
Its so simple:
After 4 minute the a was turned off means till 4 minutes a and b work together.
So,
4(1/15+i/20) = 7/15.

Let total time take = x.

Than 4 minutes after a is turned off so,

7/15+(x-4)*i/20 = 1.

x = 14 min. 40sec.

Anuraag2201 said: (Sep 5, 2014)  
For all those who do not have clue as to how to convert improper fractions to mixed fractions. :/.

Are you sure are ready for quants?

Arunkumar said: (May 19, 2015)  
@All.

Better don't confuse with the complex solutions! as, the main part of the quantitative exam is to minimize time, all should look for a shortest solution, (as given by @Kalpana) but not merely a solution (with complex steps).

For any question, a diagrammatic representation should be drawn roughly, to get a quick solutions. Also, 'learn by solving' is the key to prepare any exam.

All the best!

Vikash Patel said: (Jun 29, 2015)  
Why x-4?

Ramees said: (Feb 3, 2016)  
Easy to convert 44/3 into 14(2/3).

Divide 44 into 3 we get remainder 2(i.e 14*3 = 42).

Then we can write 14 (remainder/3) that is 14(2/3).

Neha said: (Jun 10, 2016)  
How to change the fraction value into minutes?

Sandy said: (Jul 14, 2016)  
Super solution @Kalpna.

Ashim said: (Jul 27, 2016)  
LCM of 15 & 20 is 60.
(4 + 3) * 4 = 28.
60 - 28 = 32.
4 + 32/3 =14min = 40sec.

Venky said: (Jul 10, 2017)  
Can anyone explain it in easy method?

Varsha said: (Jul 20, 2017)  
Why equating with 1?

Manisha said: (Aug 10, 2017)  
It is clear now Thank you, @Ashim.

Leela said: (Jan 14, 2018)  
Can anyone tell me why do we equate to one?

D Priya said: (Feb 1, 2018)  
@Leela.

To fulfil the condition they equate to 1. A part of work + remaining part of work = 1. To be precise, you and your friend are doing a work by sharing. You completed half the work and your friend completed half the remaining work. Ie 1/2 + 1/2 = 1.

This logic is being used in this kind of problems.

Kailash Sharma said: (Feb 18, 2018)  
a=15;
b=20;
l.c.m of 15,20=60;
a's 1Min=60/15 => 4;
b's 1Min=60/20 => 3;
(a+b)'s 4Min= (4+3)*4=28;
Now 60-28 = 32;
b remaining time = 32/3 => 10.66.
Now add 10.66+4 =>14.66.

Debalina Roy said: (Dec 19, 2018)  
"1/20 :8/15 :: 1:x " I can't understand this. Please explain me.

Vinay Kumar Gupta said: (Apr 5, 2019)  
In the question, it asks about the time required. It is not asking about total time so the answer will be 10 minute and 40 seconds.

Revant said: (Jun 6, 2020)  
@Preeti.

Very clear solution. Thanks for explaining.

Sriganesh. S said: (Jul 4, 2020)  
Can anyone explain, why they multiplying 1 in (8/15) * (1*20)?

Ezhil said: (Mar 14, 2021)  
@Sriganesh.

B can fill the tank in 1 min = 1/20 parts or work done of the tank.
After 4 min, B can alone to fill the remaining part of the tank?
min = 8/15 remaining parts or work done of the tank.
By cross multiply
1/20 parts = 1 min.
8/15 parts = ? min.
(8/15 * 1)/1/20 = ?
8/15 * 1 * 20 = ?
8/3*4 = ?
?=32/3=10 (2/3) min =10 min 40 sec (2/3 min convert to seconds 2/3 * 60=40 sec).

Thus, Total Time Required to fill the tank = 4 min + 10 min 40 sec.
= 14 min 40 sec.

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