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A solution of water and sugar is 20% sugar by weight. After several we

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Bunuel
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A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   14 Sep 2021, 08:00
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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
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A
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BrentGMATPrepNow
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A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   Updated on: 14 Sep 2021, 09:52
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Bunuel 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


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

Originally posted by BrentGMATPrepNow on 14 Sep 2021, 09:36.
Last edited by BrentGMATPrepNow on 14 Sep 2021, 09:52, edited 1 time in total.
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A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   Updated on: 14 Sep 2021, 10:10
Given: 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.
Asked: What is the ratio of the final weight of water to the initial weight of water in the mixture?

Before water evaporation: -
Water = .8k
Sugar = .2k
Total = k

After water evaporation: -
Sugar = .2k = .6T; T = k/3
Water = T - .6T = .4T = .4k/3
Total = T = k/3

The ratio of the final weight of water to the initial weight of water in the mixture = (.4k/3)/.8k = 1/6 i.e. 1:6

IMO A

Originally posted by Kinshook on 14 Sep 2021, 09:49.
Last edited by Kinshook on 14 Sep 2021, 10:10, edited 1 time in total.
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Re: A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   14 Sep 2021, 09:53
Hi BrentGMATPrepNow
(40/3)/80 = 1/6 and not 1/3
Ratio = 1:6

BrentGMATPrepNow wrote:
Bunuel 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


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)
= 1/3
= 1:3

Answer: B
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BrentGMATPrepNow
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Re: A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   14 Sep 2021, 10:00
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Kinshook wrote:
Hi BrentGMATPrepNow
(40/3)/80 = 1/6 and not 1/3
Ratio = 1:6


Thanks, I noticed that after I saw your solution. Silly mistake!

I've edited my response accordingly.

Cheers,
Brent
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KarishmaB
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Re: A solution of water and sugar is 20% sugar by weight. After several we [#permalink] New post   14 Sep 2021, 23:04
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Bunuel 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


When water evaporates, amount of water reduces but amount of sugar stays the same. If initial amount of solution was 100 ml (20 ml sugar and 80 ml water),

20 ml = Final Concentration of sugar * Final Vol (this is amount of sugar in final solution)
20 = 60% of F
20*5/3 = F

Final volume of solution is 100/3 out of which 20 ml is sugar and 100/3 - 20 = 40/3 ml is water.

Ratio is (40/3)/80 = 1/6

Answer (A)
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Re: A solution of water and sugar is 20% sugar by weight. After several we [#permalink]
14 Sep 2021, 23:04
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