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

Question

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

BrentGMATPrepNow · Answer

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

Kinshook · Answer

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

Kinshook · Answer

Hi  BrentGMATPrepNow 
(40/3)/80 = 1/6 and not 1/3
Ratio = 1:6

BrentGMATPrepNow · Answer

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

I've edited my response accordingly.

Cheers,
Brent

KarishmaB · Answer

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)

ravi1522 · Answer

Hello ,

The question is asking us to find a certain RATIO, let's start by assigning a 100ml as total 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.
remaining solution will be=20/60%
so we get value as 40/3
so water will be 40/3-20=13.33
The ratio = 13.3/80
= 1/6
= 1:6

Hence Option A is correct

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

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