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Eight liters of a 45% saline solution is left in the sun. Water evapor

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Bunuel
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Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   03 Feb 2017, 08:11
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Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters
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Re: Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   03 Feb 2017, 09:16
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Bunuel wrote:
Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters


Total Solution = 8 Lit
Salt = 3.6 Lit
Water = 4.4 Lit

\(\frac{3.6}{(8-x)} = \frac{6}{10}\)

36 = 48 - 6x

6x = 12

Or, x = 2

Thus, 2 Litres of water evaporates from the solution, answer must be (B) 2.00
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Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   Updated on: 13 Aug 2019, 21:11
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Bunuel wrote:
Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters


let w=evaporated water liters
w=.55*8-.4*(8-w)→
w=2 liters
B

Originally posted by gracie on 03 Feb 2017, 11:37.
Last edited by gracie on 13 Aug 2019, 21:11, edited 2 times in total.
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Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   08 Feb 2017, 03:44
can this be solved using weighted average method???

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Re: Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   13 Feb 2017, 08:37
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Bunuel wrote:
Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters


We are given that an 8-liter saline solution is 45% salt (and thus 55% water). Thus:

Amount of salt = 8 x 0.45 = 3.6 liters

Amount of water = 8 - 3.6 = 4.4 liters

We are also given that some amount of solution evaporates, leaving a 60% saline solution. However, since only water evaporates (salt doesn’t evaporate), we can let w be the amount of water that evaporates, and the new solution is 60% = 6/10 = 3/5 saline.

Let’s determine how much water evaporated.

3.6/(8 - w) = 3/5

5(3.6) = 3(8 - w)

18 = 24 - 3w

3w = 6

w = 2

Answer: B
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Re: Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   10 Oct 2022, 06:40
Bunuel wrote:
Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters



KarishmaB can you pls show how to solve this problem with alligation method :)
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Re: Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink] New post   10 Oct 2022, 22:09
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dave13 wrote:
Bunuel wrote:
Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?

A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters



KarishmaB can you pls show how to solve this problem with alligation method :)


"Alligation method" for me is the formula:

\(\frac{w1}{w2} = \frac{(A2 - Aavg)}{(Aavg - A1)}\)

It is the easiest way to solve weighted averages problems in most cases. The diagram could get confusing but the formula works very well.

0% and 60% were mixed together to give 45% saline solution.

\(\frac{w1}{w2} = \frac{(60 - 45)}{(45 - 0)} = \frac{1}{3} \)

So pure water : 60% saline = 1 : 3
Since total was 8 ltrs, it means 2 ltrs of water evaporated and left 6 ltrs of 60% saline.

Answer (B)
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Re: Eight liters of a 45% saline solution is left in the sun. Water evapor [#permalink]
10 Oct 2022, 22:09
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