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A certain tank is filled to one quarter of its capacity with a mixture

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A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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30 Sep 2014, 07:51
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Question Stats:

68% (01:48) correct 32% (01:42) wrong based on 598 sessions

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A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A. 43%
B. 50%
C. 52%
D. 54%
E. 56%
[Reveal] Spoiler: OA

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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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30 Sep 2014, 18:38
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NaCl................... Water ................. Total

2.4 ......................... 3.6 ....................... 6

Post evaporation

2.4 ........................... 2.6 ......................... 5

Percentage $$= \frac{2.6}{5} * 100 = 52%$$
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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30 Sep 2014, 21:54
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Bunuel wrote:
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A. 43%
B. 50%
C. 52%
D. 54%
E. 56%

The tank of 24 gallons is filled to a quarter so it had 6 gallons of water with 40% sodium chloride. In 2 hrs, .5*2 = 1 gallon of pure water (0% sodium chloride) will evaporate.
In essence, the initial mix of 6 gallons (40% sodium chloride) was a mix of 5 gallons of x% sodium chloride and 1 gallon of pure water.

Working with sodium chloride concentrations:
w1/w2 = (A2 - Aavg)/(Aavg - A1)
5/1 = (0 - 40)/(40 - x)
x = 48

So concentration of water is 100 - 48 = 52%
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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09 Jan 2015, 09:48
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Bunuel wrote:
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A. 43%
B. 50%
C. 52%
D. 54%
E. 56%

c -

initial 40% sodium = 2.4 & 60 % water = 3.6

after 2 hours- evaporating at the rate of .5/hr

sodium -2.4 [Remain same - stated],water -2.6

c- 52%

Hope i deserve some kudos
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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09 Jan 2015, 22:53
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Tank is filled 1/4 of its capacity

Solution = 1/4 * 24 = 6

Sodium = 0.4 * 6 = 2.4
Water = 6-2.4 = 3.6

Evaporation Process

0 hour - 3.6
1 hour - 3.1
2 hour - 2.6

or you can simply subtract 1 from 3.6

quantity of new solution = sodium + water = 2.4 + 2.6 = 5

Concentration of water = (2.6/5) * 100 = 52%
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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22 Oct 2016, 07:42
Here is how I did it. My mistake when i first tried it was forgetting that the tank is 1/4 full and that i needed to divide 24/4 in order to get the correct solution.

step1) (1/4) 24 = 6
step2) 6*(.40) =SC = 2.4 and 6*(.6) = W = 3.6 = total = 6
step3) 0.5*2 = 1 => 6-1 = 5 new total => 3.6 -1 = 2.6 new water
step4) 2.6/5 => (2.6*2)/(5*2) = 5.2/10 = 0.52.
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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12 Nov 2016, 00:46
Bunuel wrote:
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A. 43%
B. 50%
C. 52%
D. 54%
E. 56%

SINCE THE amount of SC didn't change we can use the formula (C final = C initial * V initial/V final)

Cf = 0.4* (6/5.5)*(5.5/5) = 48% and thus water concentration in final mix is 100%-48% 52%
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Re: A certain tank is filled to one quarter of its capacity with a mixture [#permalink]

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07 Dec 2017, 15:07
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Re: A certain tank is filled to one quarter of its capacity with a mixture   [#permalink] 07 Dec 2017, 15:07
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