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With both valves open, the pool will be filled with water in

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With both valves open, the pool will be filled with water in [#permalink]

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New post Updated on: 23 Apr 2014, 00:15
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With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10

Originally posted by arjtryarjtry on 02 Sep 2008, 02:23.
Last edited by Bunuel on 23 Apr 2014, 00:15, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: With both valves open, the pool will be filled with water in [#permalink]

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New post 23 Apr 2014, 00:15
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arjtryarjtry wrote:
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10


Let the rate of the first valve be \(x\) cubic meters per minute, then the rate of the second valve will be \(x+50\) cubic meters per minute.

As both valves open fill the pool in 48 minutes then the capacity of the pool equals to \(C=time*combined \ rate=48(x+x+50)=48(2x+50)\);
But as the first valve alone fills the pool in 2 hours (120 minutes) then the capacity of the pool also equals to \(C=time*rate=120x\);

So, \(120x=48(2x+50)\) --> \(x=100\) --> \(C=120x=12,000\).

Answer: D.
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Re: work and time [#permalink]

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New post 02 Sep 2008, 02:58
1
D. 12000 cubic meters.

If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.

Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).

or, 120x = 80 (x + 50).
or x = 100.

Hence, the capacity of pool = 120x = 12000 cubic meters.
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Re: work and time [#permalink]

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New post 02 Sep 2008, 03:14
I got the same answer (D) but used a different technique.

I made two equations
120x = y
48(2X+50) = Y

then, I substituted the values in the answer choices (starting with the middle then working my way in either direction) with y being the answer.

so if 120x=12000, then 48(2x+50)=12000 as well, which it does if you do the math; whereas if you use any other answer choice the two equations are not equal (do not have the same value for x and y)
this could be done much easier if you could use a graphing calculator finding the intercept of both lines, but these are not permitted in the GMAT.
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Re: work and time [#permalink]

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New post Updated on: 02 Sep 2008, 05:07
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?



* 9000 cubic meters
* 10500 cubic meters
* 11750 cubic meters
* 12000 cubic meters
* 12500 cubic meters
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?

Soln:
Let volume filled by first valve per minute = Va cubic meter
As first valve takes 2hours to fill the pool
therefore volume of the pool = 120 x Va....(1)

Let the volume filled by second valve per minute = Vb cubic meter

Total volume filled by both the valves in 48 minutes = Va x 48 + Vb x 48
According to the condition of the problem

Vb = Va + 50

therefore total vulme filled in 48 minutes
Va x 48 + (Va+50) x 48 = volume of the pool = 120 Va ..from (1)
or, Va = 100

Total volume of the pool = 100 x 120 = 12000 cubic meters

Option D
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Originally posted by hksingh83 on 02 Sep 2008, 04:53.
Last edited by hksingh83 on 02 Sep 2008, 05:07, edited 1 time in total.
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Re: work and time [#permalink]

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New post 02 Sep 2008, 05:02
This one took me ages to solve.

1/48 = 1/120 + x --> solve for x. x = 1/80
y(1/80) = y(1/120) + 50 --> y = 12,000
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Re: With both valves open, the pool will be filled with water in [#permalink]

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New post 22 Apr 2014, 22:31
Let 1st does in 1 minute =x so, in 120 min= 120x
2nd does=x+50
A/Q, 48x+48(x+50)=120x
X= 100
120x= 12000 (D)
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With both valves open, the pool will be filled with water in 48 minute [#permalink]

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New post 17 May 2016, 21:57
2
Responding to a pm:

With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?

(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters

Normally, I would do this question the algebra way (I wouldn't use ratios here because partial data is in time and partial in work form):

Say, capacity of the pool is x cubic meters. Consider time in minutes.

First valve rate = Work/Time = x/120

Second valve rate = x/120 + 50

Combined rate = x/48

x/48 = x/120 + x/120 + 50

x/48 - x/60 = 50

x/4 - x/5 = 12*50

x = 12*50*20 = 12000

But if I am short on time, I can take a guess.

Most probably, the rate of work will be an integer .... cubic meters per minute. The additional rate of valve 2 is 50 cubic meters per minute so it is unlikely that rate of valve 1 will be something like 150.38 cubic meters per min. It will most probably be an integer.

Assuming that, I see that only option (D) is divisible by 48.
(48 has four 2s. 9000 has three 2s, 10500 has two 2s, 11750 has one 2 and 12500 has two 2s)

So most probably answer will be 12000. Let's check.

12000/48 = 250
12000/120 = 100
Valve 1 rate is 100 cubic meters per min. Valve 2 rate is 150 cubic meters per min.
Everything matches.
Answer (D)
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With both valves open, the pool will be filled with water in [#permalink]

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New post 17 May 2016, 22:22
arjtryarjtry wrote:
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10


Hi,

I would think of this in TWO ways if I had to do this Qs WITHOUT getting into serious calculation..

1) USE of CHOICES, as also explained above-
Very helpful in many calculations..
Ofcourse here, we believe that the speed, x here, must be integer..
so total = 48(x+x+50)..
so our answer should be a multiple of 48 or 3*16...
C and E are not multiple of 3..
A and B are multiples of 3, but not of 16..
D

2) second method..
In 48 minutes, the faster valve fills up 48*50=2400 more than 1st...
If both took same time as first,that is same speed, the tank would have been filled in 1 hour..

so in 60 - 48= 12 minutes, both would have filled 2400 cum..
BUT first one alone will fill it up in 12*2 = 24 mins...
if the first fills up 2400 in 24 mins..
it will fill 100 in 1 min and 12000 in 120 mins or 2 hours..
so Capacity of tank = 12000cum

D
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With both valves open, the pool will be filled with water in [#permalink]

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New post 25 Sep 2016, 07:45
Maybe you could try this way :)

Let us consider 240 unit water filled by valve.
(I took the LCM of 48 and 120 minute - 2 Hour).

Valve A - 2 Hour - 120 minute.
Rate - 2 unit/minute (As we have consider total unit 240 and valve A took 120 minute, so rate is 240/120 = 2.)
Valve A+B - 48 Minute.
Rate - 5 unit/minute (as specified above)

So, Value B alone takes 3 unit/minute. (5 unit/minute of a+b together - 2 unit/minute A alone.)
So time taken by B to fill 240 unit of tank is 80 minute. (240/3 - 80 minute ).
Now, as per question second valve emits 50 cubic meters of water more than the first every minute.
Every minute water emit by valve B is :- 50 * 3 = 150 cubic meter/ minute. so for 80 minute - 150 * 80 = 12000 cubic meter.
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Re: With both valves open, the pool will be filled with water in [#permalink]

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New post 25 Sep 2016, 11:09
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

let c=capacity of pool
c/120+(c/120)+50=c/48
.5c=6000
c=12,000 cubic meters
D.
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Re: With both valves open, the pool will be filled with water in [#permalink]

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Re: With both valves open, the pool will be filled with water in   [#permalink] 09 Apr 2018, 05:14
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