GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Aug 2020, 14:00 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Two pipes can separately fill a tank in 20 hours and 30 hours

Author Message
TAGS:

### Hide Tags

General GMAT Forum Moderator V
Joined: 15 Jan 2018
Posts: 982
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37 Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

4
1
13 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:27) correct 32% (02:52) wrong based on 209 sessions

### HideShow timer Statistics

Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

_________________
General GMAT Forum Senior Moderator | D-Day: ‎Tuesday, October 20, 2020‎ | 12:00 PM

Should I retake GMAT? Retaking GMAT Strategies!

What Are My Chances - Automated Profile Evaluation Tool is Here!
Director  P
Joined: 04 Aug 2010
Posts: 684
Schools: Dartmouth College
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

3
3
DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Let the tank = 180 gallons.

Since the first pipe takes 20 hours to fill the 180-gallon tank, the rate for the first pipe$$= \frac{work}{time}= \frac{180}{20} = 9$$ gallons per hour.
Since the second pipe takes 30 hours to fill the 180-gallon tank, the rate for the second pipe $$= \frac{work}{time} = \frac{180}{30} = 6$$ gallons per hour.
Combined rate for the two pipes = 9+6 = 15 gallons per hour.

$$\frac{1}{3}$$ of the 180-gallon tank $$= \frac{1}{3}*180 = 60$$ gallons.
Since the combined rate for the two pipes = 15 gallons per hour, the time for the two pipes to pump in 60 gallons $$= \frac{work}{rate} = \frac{60}{15} = 4$$ hours.

Remaining volume = 180-60 = 120 gallons.
Since the leak reduces the rate by 1/3, the resulting rate $$= \frac{2}{3}*15 = 10$$ gallons per hour.
Since the new rate = 10 gallons per hour, the time for the remaining 120 gallons $$= \frac{work}{rate} = \frac{120}{10} = 12$$ hours.

Total time to fill the tank = (4 hours for the first 1/3 of the tank) + (12 hours for the remaining volume) = 4+12 = 16 hours.

_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
##### General Discussion
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3248
Location: India
GPA: 3.12
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

2
2
DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Let's assume the size of the tank to be LCM(20,30) = 60 units.
The individual rates of the two pipes filling are 3 units & 2 units respectively.

Together the tanks fill 5 units in an hour. When the tank is $$\frac{1}{3}$$rd full(20 units have been filled). The leak develops
causing the tank to fill at $$\frac{2}{3}$$rds of its usual rate. The time taken to fill the first 20 units is $$\frac{20}{5} = 4$$ hours.

For the remaining 40 units, the tanks will fill $$\frac{10}{3}(5*\frac{2}{3})$$ units in an hour.
Because of the leak. the pipe takes $$\frac{40}{\frac{10}{3}} = \frac{120}{10} = 12$$ hours to fill the remaining tank.

Therefore, the total time taken for the two pipes to fill the tank is 4 + 12 = 16 hours(Option C)
_________________
You've got what it takes, but it will take everything you've got
Intern  B
Joined: 28 Aug 2018
Posts: 12
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

2
1
Pipe A - can fill the tank in 20 hrs. Hence, in 1 hr it can fill 1/20th of the tank.
Pipe B - can fill the tank in 30 hrs. Hence, in 1 hr it can fill 1/30th of the tank.

Therefore, when both pipes are opened, (1/20 + 1/30 =) 1/12th of the tank is filled in an hr. It'll take both the pipes 12 hrs to fill the tank completely.

When 1/3rd of the tank is filled, both the pipes would have been opened for (1/3 = 4/12 = 4*(1/12)) 4 hrs.
Now, 2/3rd (= 8/12) of the tank remains to be filled.

However, at this stage due to the leak in the tank, 1/3rd of the water supplied by the pipes leaks.
So, now only (2/3 * 1/12 = ) 1/18th of the tank is filled in an hour instead of 1/12th earlier.
At this rate it would have taken 18 hrs to fill the tank if it were completely empty.
However, since only 8/12th of the tank needs to be filled, it'd take another (8/12 * 18 =) 12 hrs to completely fill the tank.

Therefore, the tank would be completely filled in (4 + 12 =) 16 hrs.
RSM Erasmus Moderator V
Joined: 26 Mar 2013
Posts: 2493
Concentration: Operations, Strategy
Schools: Erasmus
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

GMATGuruNY wrote:
DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Let the tank = 180 gallons.

Since the first pipe takes 20 hours to fill the 180-gallon tank, the rate for the first pipe$$= \frac{work}{time}= \frac{180}{20} = 9$$ gallons per hour.
Since the second pipe takes 30 hours to fill the 180-gallon tank, the rate for the second pipe $$= \frac{work}{time} = \frac{180}{30} = 6$$ gallons per hour.
Combined rate for the two pipes = 9+6 = 15 gallons per hour.

$$\frac{1}{3}$$ of the 180-gallon tank $$= \frac{1}{3}*180 = 60$$ gallons.
Since the combined rate for the two pipes = 15 gallons per hour, the time for the two pipes to pump in 60 gallons $$= \frac{work}{rate} = \frac{60}{15} = 4$$ hours.

Remaining volume = 180-60 = 120 gallons.
Since the leak reduces the rate by 1/3, the resulting rate $$= \frac{2}{3}*15 = 10$$ gallons per hour.
Since the new rate = 10 gallons per hour, the time for the remaining 120 gallons $$= \frac{work}{rate} = \frac{120}{10} = 12$$ hours.

Total time to fill the tank = (4 hours for the first 1/3 of the tank) + (12 hours for the remaining volume) = 4+12 = 16 hours.

Dear GMATGuruNY

I do not understand the reasoning behind the leak in the tank and the be 2/3 of the combines rate of both pumps?

does not the leak produce 1/3 of the water supplied to lost, lowering the water to 40 (1/3 * 60 =20 so remaining water to be 40)?

Can you please elaborate more? I'm confused.

Thanks
Director  V
Joined: 25 Dec 2018
Posts: 651
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

GMATGuruNY wrote:
DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Let the tank = 180 gallons.

Since the first pipe takes 20 hours to fill the 180-gallon tank, the rate for the first pipe$$= \frac{work}{time}= \frac{180}{20} = 9$$ gallons per hour.
Since the second pipe takes 30 hours to fill the 180-gallon tank, the rate for the second pipe $$= \frac{work}{time} = \frac{180}{30} = 6$$ gallons per hour.
Combined rate for the two pipes = 9+6 = 15 gallons per hour.

$$\frac{1}{3}$$ of the 180-gallon tank $$= \frac{1}{3}*180 = 60$$ gallons.
Since the combined rate for the two pipes = 15 gallons per hour, the time for the two pipes to pump in 60 gallons $$= \frac{work}{rate} = \frac{60}{15} = 4$$ hours.

Remaining volume = 180-60 = 120 gallons.
Since the leak reduces the rate by 1/3, the resulting rate $$= \frac{2}{3}*15 = 10$$ gallons per hour.
Since the new rate = 10 gallons per hour, the time for the remaining 120 gallons $$= \frac{work}{rate} = \frac{120}{10} = 12$$ hours.

Total time to fill the tank = (4 hours for the first 1/3 of the tank) + (12 hours for the remaining volume) = 4+12 = 16 hours.

Is there any specic reason to take tak capacity as 180 gallons?(LCM formula?)
Director  P
Joined: 04 Aug 2010
Posts: 684
Schools: Dartmouth College
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

1
Mo2men wrote:
Dear GMATGuruNY

I do not understand the reasoning behind the leak in the tank and the be 2/3 of the combines rate of both pumps?

does not the leak produce 1/3 of the water supplied to lost, lowering the water to 40 (1/3 * 60 =20 so remaining water to be 40)?

Can you please elaborate more? I'm confused.

Thanks

Prompt:
When the tank is 1/3 full, a leak develops through which 1/3 of the water supplied by both the pipes leaks out.
This wording is intended to convey the following:
Once the tank is 1/3 full, a leak develops.
This leak decreases the input rate, as follows:
For every 3 gallons supplied by the two pipes, the leak removes 1/3 of the 3 gallons.
In other words, the leak removes 1 gallon for every 3 gallons supplied by the two pipes, reducing the input rate by 1/3.
The resulting input rate is thus 2/3 of the original input rate.
_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
Director  P
Joined: 04 Aug 2010
Posts: 684
Schools: Dartmouth College
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

1
mangamma wrote:

Is there any specic reason to take tak capacity as 180 gallons?(LCM formula?)

The capacity must be divided by the two given times (20 hours and 30 hours) and then by 3 (since the rate is reduced by 1/3).
To get a good value for the capacity, I multiplied the LCM of 20 and 30 by 3:
LCM (20,30) * 3 = 60*3 = 180
_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1675
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

mangamma wrote:
GMATGuruNY wrote:
DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Let the tank = 180 gallons.

Since the first pipe takes 20 hours to fill the 180-gallon tank, the rate for the first pipe$$= \frac{work}{time}= \frac{180}{20} = 9$$ gallons per hour.
Since the second pipe takes 30 hours to fill the 180-gallon tank, the rate for the second pipe $$= \frac{work}{time} = \frac{180}{30} = 6$$ gallons per hour.
Combined rate for the two pipes = 9+6 = 15 gallons per hour.

$$\frac{1}{3}$$ of the 180-gallon tank $$= \frac{1}{3}*180 = 60$$ gallons.
Since the combined rate for the two pipes = 15 gallons per hour, the time for the two pipes to pump in 60 gallons $$= \frac{work}{rate} = \frac{60}{15} = 4$$ hours.

Remaining volume = 180-60 = 120 gallons.
Since the leak reduces the rate by 1/3, the resulting rate $$= \frac{2}{3}*15 = 10$$ gallons per hour.
Since the new rate = 10 gallons per hour, the time for the remaining 120 gallons $$= \frac{work}{rate} = \frac{120}{10} = 12$$ hours.

Total time to fill the tank = (4 hours for the first 1/3 of the tank) + (12 hours for the remaining volume) = 4+12 = 16 hours.

Is there any specic reason to take tak capacity as 180 gallons?(LCM formula?)

Yes, this is the only reason this value has been chosen. You could also take 60 (LCM of 20 & 30), but that would become a fraction after initial division. So, choose LCM of 20 and 30 and multiply it by 3.

Means 60 * 3 = 180

This way you can get rid of fractions and can increase you calculation speed.
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Intern  B
Joined: 27 Nov 2018
Posts: 30
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

Work rate formula: AB/(A+B)=T(for both to work together)
20x30/(20+30)=12
While working simultaneously, it takes the two pipes 12 hours to fill the tank.
Given 1/3 of the water filled by the pipes are lost, meaning 12x(1/3) of time is wasted, =4 hours.
So, it takes an additional 4 hours to fill the tank: 12+4=16hours.
RSM Erasmus Moderator V
Joined: 26 Mar 2013
Posts: 2493
Concentration: Operations, Strategy
Schools: Erasmus
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

Hi DisciplinedPrep

I hope you are doing well in GMAT prep as your nickname says. What is the source of the question? it is really good.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 6509
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

let total capacity of tank = 60 ltrs
so rate of A = 60/20 ; 3 and rate of B = 60/3 ; 2
together ; 5
given 1/3 of tank is filled ; i.e 20 ltrs ; so time taken would have been 20/5 ; 4 hrs
and later leak happens and the rate decreases by 1/3 or original value or say the rate becomes 2/3 so new combined flow rate 5*2/3 ; 10/3
so for 40 ltrs balance vol the time it will take
40/10 /3 ; 12 hrs
total time taken 12 + 4 ; 16 hrs
IMO C
Intern  B
Joined: 30 Aug 2018
Posts: 6
Location: Germany
GPA: 2.8
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

First post gmatclub. I guess this is a positive sign. ^^

Well, I did it in this way:

Rate of pipe A: 1/20
Rate of pipe B: 1/30

Both pipes are opened to fill the tank; so combined rate is 5/60 or 1/12

Combined rate is 1/12 so tank will be full after 12h.

When the tank is 1/3 full a leak develops in the tank through which 1/3 of the water leak out
Translated: When tank is at 4/12 all the water leaks out. (This is after 4 Hours)

So there are 4 extra hours to add because of the leak.

12h+4h = 16h

Intern  B
Joined: 16 Mar 2020
Posts: 17
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

DM Me to know the simple method.

Let us assume capacity of the tank is 600 Liters.
Efficiency of pipe 1 - 30 L/H
Efficiency of Pipe 2 - 20 L/H

Pipe 1 + Pipe 2 = 50 L/H which means Tank will take 12 H to fill it if there is no leak.

now Opening C will leak 200 Liters from tank which means another 200/50 i.e 4 Hrs to fill the void

hence total 12 + 4 = 16 HRS.

Hope it helps!!

Vikas Singla
_________________

Vikas Singla
Manager  S
Status: BELIEVE IN YOURSELF
Joined: 06 Oct 2019
Posts: 98
Location: India
Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

Puyol wrote:
First post gmatclub. I guess this is a positive sign. ^^

Well, I did it in this way:

Rate of pipe A: 1/20
Rate of pipe B: 1/30

Both pipes are opened to fill the tank; so combined rate is 5/60 or 1/12

Combined rate is 1/12 so tank will be full after 12h.

When the tank is 1/3 full a leak develops in the tank through which 1/3 of the water leak out
Translated: When tank is at 4/12 all the water leaks out. (This is after 4 Hours)

So there are 4 extra hours to add because of the leak.

12h+4h = 16h

I have also done this in the same way as you did but don't know everyone started calculating the rate of water loss due to leak in the tank.

I assumed the leak got sealed after the tank empty due to leak.
VP  D
Joined: 07 Dec 2014
Posts: 1260
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

DisciplinedPrep wrote:
Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank, but when the tank is 1/3 full a leak develops in the tank through which 1/3 of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?

A. 15 hours
B. 25 hours
C. 16 hours
D. 12 hours
E. 10 hours

combined rate=1/20+1/30=1/12
12/3=4 hours to fill 1/3 of tank before leak
let t=time to fill tank after leak
t*(1/12)(2/3)=2/3→
t=12 hours+4 original hours=16 total hours to fill tank
C
Intern  B
Joined: 20 Aug 2017
Posts: 37
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

A: 1/20. B: 1/30. A+B: 1/12 (they are filling the tank in 12 hours).

Suppose the tank is 180 liters, then they fill 15 liters each hour.

Now, they worked (12*1/3) 4 hours and filled (180*1/3) 60 liters - we are left with (180-60) 120 liters to be filled.

From now on, their rate changes to (10*2/3) 10 liters per hour to fill 120 liters. It will take A&B (120/10) 12 hours to fill the rest of the tank.

C: 12+4 = 16.
Manager  S
Joined: 30 Jun 2019
Posts: 239
Re: Two pipes can separately fill a tank in 20 hours and 30 hours  [#permalink]

### Show Tags

Break into into parts
A and B work to fill the tank 1/3
A and B work together against the leak to fill 2/3

A and B together
1/3 = (1/20+1/30)t
t=4

AB against leak
2/3 = (1/20+1/30)t - 1/3(1/20+1/30)t
t=12

12+4=16 Re: Two pipes can separately fill a tank in 20 hours and 30 hours   [#permalink] 13 Jul 2020, 15:14

# Two pipes can separately fill a tank in 20 hours and 30 hours  