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# A solution of salt and water is 10 percent salt by weight. After a per

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Posts: 52390
A solution of salt and water is 10 percent salt by weight. After a per  [#permalink]

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26 Apr 2018, 12:27
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Difficulty:

55% (hard)

Question Stats:

60% (02:24) correct 40% (01:59) wrong based on 89 sessions

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A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1

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Re: A solution of salt and water is 10 percent salt by weight. After a per  [#permalink]

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26 Apr 2018, 13:00
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Bunuel wrote:
A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1

We'll use easy numbers to help avoid confusing calculations.
This is an Alternative approach.

Say our solution is 100L. Then there are 10L worth of salt.
After the evaporation, these 10L are now 40% of the solution so the total volume is 10/40% = 10*100/40 = 10*2.5 = 25L
Then we had 100-10 = 90L of water at the start and 25 - 10 = 15L of water at the end.
So the ratio is 90 : 15 = 6 : 1

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Re: A solution of salt and water is 10 percent salt by weight. After a per  [#permalink]

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26 Apr 2018, 20:20
Bunuel wrote:
A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1

let 10=total units of original solution
let w=water evaporated
.9*10-w=.6(10-w)
w=7.5
initial water weight=.9*10=9
final water weight=.6*(10-7.5)=1.5
9/1.5=6 to 1
E
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Re: A solution of salt and water is 10 percent salt by weight. After a per  [#permalink]

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26 Apr 2018, 23:41
Bunuel wrote:
A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1

Ans: E

Given ratio of salt to water= S: W =10:90 we can also write it this way. S/W=10/90=1/9 ; S=W/9
After evaporation water's quantity changed (lets say became W') but Salt's remains the same(S) so S/W'= 40/60 =4/6
by putting S=W/9 we get W/W'*9=4/6
we need to find W/W' so from this we get W/W'= (9*4)/6 = 6/1 so ratio is (6 to 1)

Ans: E
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Re: A solution of salt and water is 10 percent salt by weight. After a per  [#permalink]

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30 Apr 2018, 15:28
Bunuel wrote:
A solution of salt and water is 10 percent salt by weight. After a period of time under pressure and heat, a portion of the water evaporates so that the solution is 40 percent salt by weight. What is the ratio of the initial weight of water to the final weight of water in the solution?

(A) 1 to 6
(B) 1 to 4
(C) 1 to 3
(D) 4 to 1
(E) 6 to 1

We can create the following ratio:

salt : water = 1x : 9x

Now we let w = weight of water evaporated, and we convert 40% to its decimal equivalent of 2/5. We can create the equation:

x/(10x - w) = 2/5

5x = 20x - 2w

2w = 15x

w = 7.5x

The amount of water left is 9x - 7.5x = 1.5x and, thus, the ratio of the initial weight of water to the final weight of water in the solution is 9x/1.5x = 9/1.5 = 90/15 = 6/1.

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Re: A solution of salt and water is 10 percent salt by weight. After a per &nbs [#permalink] 30 Apr 2018, 15:28
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