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A solution of water and sugar is 20% sugar by weight. After several we
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07 Sep 2021, 07:40
07 Sep 2021, 07:40
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A solution of water and sugar is 20% sugar by weight. After several weeks, some of the water evaporates so that the solution is 60% sugar by weight. What is the ratio of the final weight of water to the initial weight of water in the mixture?
(A) 1:6
(B) 1:3
(C) 1:4
(D) 4:1
(E) 6:1
(A) 1:6
(B) 1:3
(C) 1:4
(D) 4:1
(E) 6:1
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Re: A solution of water and sugar is 20% sugar by weight. After several we
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11 Nov 2021, 12:46
11 Nov 2021, 12:46
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Carcass wrote:
A solution of water and sugar is 20% sugar by weight. After several weeks, some of the water evaporates so that the solution is 60% sugar by weight. What is the ratio of the final weight of water to the initial weight of water in the mixture?
(A) 1:6
(B) 1:3
(C) 1:4
(D) 4:1
(E) 6:1
(A) 1:6
(B) 1:3
(C) 1:4
(D) 4:1
(E) 6:1
The question is asking us to find a certain RATIO, let's start by assigning a "nice" value to the original volume of solution
A solution of water and sugar is 20% sugar by weight.
Let's say that we ORIGINALLY have 100 ml of solution.
20% of 100 = 20
So, the original solution contains 20 ml of sugar, and 80 ml of water
After several weeks, some of the water evaporates so that the solution is 60% sugar by weight.
Let x = the volume of water in the NEW solution.
Since no sugar was evaporated from the mixture, we know that the new solution still contains 20 ml of sugar.
So, the total volume of the NEW solution = x + 20
Since the new solution is 60% sugar by weight, we can write: 20/(x + 20) = 60/100
Simplify to get: 20/(x + 20) = 3/5
Cross multiply: 3(x + 20) = 100
Expand: 3x + 60 = 100
Subtract 60 from both sides: 3x = 40
Solve: x = 40/3
What is the ratio of the final weight of water to the initial weight of water in the mixture?
The ratio = (40/3)/80
= (40/3)(1/80)
= 1/6
= 1:6
Answer: A
General Discussion
A solution of water and sugar is 20% sugar by weight. After several we
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07 Sep 2021, 07:57
07 Sep 2021, 07:57
4
Let's say we have a \(100\) ml solution at the start.
\(20\)% sugar by weight so sugar = \(20\) & water = \(80\) ml
After several weeks, water evaporates and the volume of sugar = \(60\)% by weight
so \(20\) of sugar will represent \(60\)% of the solution so total solution \(= 33\frac{1}{3}\)
final weight of water \(= \frac{100}{3} - 20 = \frac{40}{3}\)
Required ratio = \(\frac{40}{3}\)*\(\frac{1}{80}\) \(= 1:6\)
Answer A
\(20\)% sugar by weight so sugar = \(20\) & water = \(80\) ml
After several weeks, water evaporates and the volume of sugar = \(60\)% by weight
so \(20\) of sugar will represent \(60\)% of the solution so total solution \(= 33\frac{1}{3}\)
final weight of water \(= \frac{100}{3} - 20 = \frac{40}{3}\)
Required ratio = \(\frac{40}{3}\)*\(\frac{1}{80}\) \(= 1:6\)
Answer A
