Aptitude - Pipes and Cistern - Discussion

6. 

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

[A]. 60 gallons
[B]. 100 gallons
[C]. 120 gallons
[D]. 180 gallons

Answer: Option C

Explanation:

Work done by the waste pipe in 1 minute = 1 - 1 + 1
15 20 24

    = 1 - 11
15 120

    = -  1 .    [-ve sign means emptying]
40

Volume of 1 part = 3 gallons.
40

Volume of whole = (3 x 40) gallons = 120 gallons.


Shankarbalaji said: (Dec 26, 2010)  
2 pipes can fill a tank in X and Y times respectively. How to calculate the time taken to fill the tank if both the pipes a open together?

Zonked said: (Jan 4, 2011)  
i dont get this one.

Karan Ratnaparkhi said: (Jan 7, 2011)  
As per the given condition we have 1/20 + 1/24 + 1/3 = 1/15. Here 1/3 refers to waste pipe nd 1/20, 1/24 refer to other 2 pipes.

Sravanreddypailla said: (May 5, 2011)  
Two pipes can fill a tank in 20 and 24 minutes respectively and part filled by them is(1/20+1/24)

1gallon=~4litres

All the three pipes working together total tank fills in 15min
so 1part fills in 15min


waste pipe can empty 3 gallons per minute so the volume of tank emptying by waste pipe is total filled tank minus part filled by to pipes i.e 1/15-(1/20+1/24) x 1min= -1/40

that means in 1min waste pipe is emptying 1/40part of total tank

given ,
waste pipe can empty 3 gallons per minute

therefore total volume is 1/40=3 gallons=>120 gallons

hence capacity of tank is 120 gallons

Manasa said: (Jun 11, 2011)  
Thanks a lot. SRAVANREDDYPAILLA.

Raj said: (Apr 11, 2012)  
How did 1/20+1/24=11/120.
Please explain it ?

Rabi said: (Apr 18, 2012)  
Let the capacity of tank x gallons. then in 1 minute tank filled (x/20+x/24-3)gallons
From the question we can write
15(x/20+x/24-3)=x [it took 15 min to fill x gallons]
x/20+x/24-x/15=3
(6x+5x-8x)/120=3
3x/120=3
x=120 gallons

Poonam said: (Feb 14, 2013)  
What is mean by galloons?

Sowmi said: (Feb 20, 2013)  
A measure of capacity for liquids. Say water or milk can be measured on gallons.

Krish said: (Apr 27, 2013)  
Let x = no.of minutes to take empty the gallon by leakage.

(1/20+1/24-1/x)=1/15.

x will get = 40 min.

40*3 = 120 gallon.

Mouni said: (Jan 4, 2015)  
How did -1/40? Please explain it.

Rupinder Kaur said: (Jan 5, 2015)  
How did 11/120?

Arshiya said: (Mar 13, 2015)  
11/120 is the time taken by two pipes to fill the tank.

Bhakta B Monger said: (Jul 9, 2015)  
A = 20 minutes.
B = 24 minutes.
C = 3 gallons per minute.

*The statement states that all three pipes working together can fill the tank in 15 minutes.

Therefore we can express it as : A+B+C = 15 minutes.

Say A+B+C=X.
Then C = X- (A+B).
Hence C = 15 minutes - (A+B).

Making the values in the ratio one we get.

C = 1/15- (1/20 + 1/24).
= 1/15 - 11/120.
= - 3/120.
= -1/40.

Thus the part filled by pipe C = 40 minutes.

For the volume of tank:

Given:

Pipe C = 3 gallons per minute.

Which means, in 1 minute = 3 gallons.

Then in 40 minutes = x.

x = 40*3 = 120 gallons.

Dwarikesh Sharma said: (Jul 30, 2015)  
(1/20)+(1/24)-3G = (1/15).

-3G = (1/15)-(1/20+1/24).

-3G = -3/120.

G = 1/120.

Capacity of Tank G=120 gallon.

Sujit Baji said: (Aug 19, 2015)  
(1/15 - 11/120) = -1/40 how? please explain it.

Ragi said: (Nov 7, 2015)  
15(x/20+x/24-3) = x.
(11x-120)/8 = x.
x = 40 gallon.

Aniket said: (Dec 17, 2015)  
You can simply take the L.C.M of the values and get the result.

L.C.M of above values = 2x2x2x3x5 = 120.

Sreeram said: (Feb 8, 2016)  
A and B.

Time: 20min and 24min.

Efficiency: 6 and 5.

Work done A+B in 1 min = 11.

Work done A+B in 15 min = 11*15 = 165.

Tank emptied by C in 15 min = 45.

= 165 - 45 = 120 gallons.

Snhk said: (Feb 17, 2016)  
L.C.M of 20, 15, 24 = 120 unit total capacity.

1st pipe = 6 unit.

2nd pipe = 5 unit.

= 11 unit.

Total 120/15 = 8 unit.

3rd (-) pipe capacity = (11 - 8) = 3 unit.

As UTC 120.

3rd pipe can empty = 120/3 = 40 unit which is = 3 gallons per minute.

Hence the capacity of the tank (40*3) =120 gallons.

Nitin said: (Jun 15, 2016)  
L.C.M of 20, 15, 24 = 120 unit total capacity.

120/3 = 40.
40 * 3 = 120.

Sindhu said: (Jun 28, 2016)  
Why making the values in the ratio one we get.

C = 1/15 - (1/20 + 1/24).

S.N.Raju said: (Jul 20, 2016)  
Given,

First pipe takes 20h.
Second pipe take 24h.

ALL together take 15h.

Assuming that capacity of tank L. C. M [20, 24, 15] = 120.

First pipe can fill 6u/m.
Second pipe fill 5u/m.

All three fill 8u/m -------> 1.

First and second together fill in 11m/u----------> 2.

From 1 and 2 we get;

Third pipe fills the tank in 3u/m that is 120/3 = 40u of total fill.

But given 3 gallons are empty.

3 * 40 = 120gallons (capacity of tank).

Ashutosh Sahani said: (Jul 21, 2016)  
120 gallon is waste water, which drains out from the tank in 15 min.

Nasir said: (Aug 16, 2016)  
Let, the capacity of the tank is x gallon.

3 pipes 1 min can fill up (1 / 20 +1 / 24 - 3),

So, 15 min can fill up, 15 (1 / 20 + 1 / 24 - 3),

We get 15 (1 / 20 + 1 / 24 - 3) equally to x.

We get the calculation of x is 120 gallons.

Aqueeb Khan said: (Sep 4, 2016)  
How can we solve this problem by the unitary method?

Md.Gohor Rizvi. said: (Oct 17, 2016)  
Let the capacity of the tank or pump X gallons.
The first pipe can fill the tank in 20 min.
The second pipe can fill the tank in 24 min.
1st pipe 20 min. fill X gallon. So, First pipe in one min can fill X/20 gallons.
So, the second pipe can fill in X/24 gallons.
And the third pipe flows out 3 gallons per minute.
So, X/20 + X/24 - 3 equal X/15 therefore X equal 120 gallons.

Siddhesh said: (Apr 20, 2017)  
The part of tank filled in 1 min by all pipes=(1/20)+(1/24)-(1/x).
= (44x-480)/480x.

The time required to fill 1 tank.
= 480x/(44x-480) minutes.

Where, x = time in minutes required to empty the tank by the waste pipe.
But all pipes fill the total tank in 15 minutes.

So, 15 = 480x/(44x-480).
x = 40 minutes.

The capacity of tank = discharge per minute * time.
= 3 * 40,
= 120 gallons.

Pritesh Bhawsar said: (Jul 27, 2017)  
I have the best solution here.
take LCM of 20,24 = 120

Pipe c can empty 3 gallon/minute.
120/3 = 40 minute.
-----------------------------|
minute | efficiency |
-------------|---------------|
a = 20 | 6 |
b = 24 | 5 |
c = 40 | 3 |
******************************
(a+b-c) --> 11-3 = (+8)

120/8 = 15 minute.

120-gallon tank will fill in 15 minutes,
A can fill in 24 minutes or 5 gallons/minute,
B can fill in 20 minutes or 6 gallons/minute.

C can empty in 40 minutes or 3 gallons/minute <---question says.

Tubai said: (Jul 27, 2017)  
Your logic is most acceptable or easy to me, Thanks @Rabi.

Prasna said: (Jan 3, 2018)  
Take the LCM of 24 and 20, you will get the Answer is 120.

Puja Banerjee said: (Jan 25, 2018)  
Thanks for the explanation @Bhakta B Monger.

Swapnil said: (Feb 7, 2018)  
Let , the time taken by waste pipe to empty the tank is x.

Then part feed in one min.
(1/20+1/24) - 1/X = 1/15
11/120 -1/X = 1/15,
11X-120/120X = 1/15,
165X -1800= 120 X,
By solving we get x = 40 min.
So 40 min is the time which is taken by waste pipe to empty the entire tank

In problem it is given that waste pipe discharge 3 gallons per min.
40*3= 120 gallons is a capacity of tank.

Somi said: (May 22, 2018)  
Thank you @Swapnil.

Somi said: (May 22, 2018)  
Thank you @Swapnil.

Rakhshanda said: (Jul 29, 2018)  
How 3 gallons =1/40?

Vishal Gawali said: (Aug 7, 2018)  
We can directly determine the total capacity of tank by taking LCM of 20 24 15 as 120.

Shyam said: (Feb 3, 2019)  
How this relation come 1/A+1/B+1/C = 1/15?

Third pipe can empty tank that means 1/A+1/B-1/C = 1/15.

Bagga said: (Jun 8, 2019)  
A=20m, B=24m, Let c=x min.

Now LCM= 120x(Let Capacity of Tank).

Part filled per min:
A = 6x.
B = 5x.
C = 120.

Now given tank filled in 15 min.
therefore, 120x/11x-120 = 15.
solve this x = 40.

Now given C fills 3 Gallon in 1 min which is its efficiency.

Hence 40 * 3 = 120 Capacity of Tank.

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