How many liters of water must be evaporated from 50 liters of a 3-perc

Question

How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 10-percent solution?

A) 35
B) 33 1/3
C) 27
D) 16 2/3
E) 15

Source: Chili Hot GMAT

PareshGmat · Accepted Answer

Answer = A) 35

Water..................... Sugar ................... Total

48.5 ......................... 1.5 ...................... 50 (3% sugar concentration)

48.5 - x .................... 1.5 ......................... 50 - x (Say "x" is the amount of water removed from the solution)

Sugar should constitute 10% of the solution post water removal

\frac{10}{100} (50-x) = 1.5

x = 50-15 = 35

hopeful101candidate · Answer

How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 10-percent solution?

3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 10% of the solution. Set up an inequality and solve for x:

1.5/x = 1/10

x = 15

Since you need a 15L solution, you must evaporate 35 of the original 50L solution to get a 10% solution.

Answer is A.

usre123 · Answer

Don't know why but it took me a long time to solve...

(1.5/ total) *100 =10
therefore 1.5/T =1/10

T=15.
in order to go from 50l to 15l, we need to evaporate 35 litres.

Therefore A

intheend14 · Answer

We start with 1.5L of sugar and 48.5L of water. This is a 3% sugar solution. To get to a 10% sugar solution, we need 1.5L sugar per 15L of total volume or 13.5L of water. Just evaporate 48.5-13.5=35L of water.

Choice A

Choice A

amitshri15 · Answer

In 50 ltr we have 50 * (3/100) = 1.5 sugar. Now after evaporation 1.5 sugar should be 10%. 
So 1.5 = (50-x) 10/100 => x= 35.

Answer is A.

vards · Answer

Hey ,
could anyone please tell me why shouldnt we substract  x  FROM 1.5 as well here , since a part of solution is removed from main solution. When we remove and replace the solution, we remove that part ofsolution from LHS as well as RHS of the equation.

Kind Regards,
Vardhaman

PareshGmat · Answer

1.5 is 100% sugar concentrate. We cannot remove "only sugar" from the liquid mixture, so it remains as it is.

The equation setup is for the concentration to evaluate value of x.

Yes, you can see in the table that from the total of 50, "x" was removed (Here LHS/RHS is taken into account)

vards · Answer

Hi Paresh. Thanks for the reply.

Yes i understand, but the solution contains sugar. So, when the solution evaporates, the sugar within the solution should also evaporate.

I mean , suppose=100 litres of water has 10 percent concentration of alcohol. so when 50 percent of the solution evaporates, it means 50 litres of solution will evaporate which will contain 5 litres of alcohol. In the same context here, i thought sugar should also evaporate from solution in equal proportion.

Please clear my doubt. Many Thanks.

PareshGmat · Answer

Sugar cannot evaporate. Only "water content" in the solution evaporates.

100 Litres of 10% alcohol solution = 90 Litres of water + 10 Litres of Alcohol (Pure alcohol, 100%; NO water)

50% solution evaporates; so resultant would be

(100-50) Litres of solution = (90-50) Litres of water + 10 Litres of Alcohol

50 Litres of solution = 40 Litres of water + 10 Litres of Alcohol

As quantity of alcohol remains same, its concentration is now 20% in the solution

HKD1710 · Answer

x litre evaporated.

old concentration = new concentration
50 * 3/100 = (50-x) * 10/100
X=35
Answer is A.

sasyaharry · Answer

50L of solution contains 3% sugar, i.e 1.5L
The rest(97%) is water, 50-1.5 = 48.5L

In order to get a target solution that is 90% water, we need to remove some water. Let this be 'X' liters.
Hence, the equation becomes:
48.5 - x = 0.9(50-x)
3.5=0.1x
x = 35 L

coylahood · Answer

Use the following formula:

(V1/V2)*C1=C2 (1)
Where V1 = original volume
V2 = Volume after evaporation 
C1 = original concentration
C2 = new concentration

V1 = 50
C1 = 3%
C2= 10%
Let x = quantity of water evaporated
Therefore V2 = 50-x 
Substituting in equation 1 we get

(50*3)/(50-x)=10
150 = 500-10x
10x = 350 
x = 35.
Therefore A is the correct Answer.

satya2029 · Answer

balance sugar
50*0.03=(50-X)0.10
X=35 Litres
A:)

gracie · Answer

let w=liters of water to be evaporated
(.97*50)-w=.9(50-w)→
w=35 liters
A

dave13 · Answer

KarishmaB using alligation method sugar water 3.............0 .......10...... 10...........7 so sugar to water is 10 to 7 Water is \frac{7}{17} *50 getting wrong answer however if i multiply like this \frac{7}{10}*50 = 35 i get correct answer but shouldnt it be 7/17 *50 ? why ?

KarishmaB · Answer

I don't know how you got sugar to water as 10:7 but I like to simply use the formula given below:

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

Mixing two solutions is the same as separating them. The formula can be used for mixing water with 10% sugar sol to get 3% sugar sol as well as for separating 3% sugar sol into 10% sugar sol and evaporated water.

\frac{w1}{w2} = \frac{(10 - 3)}{(3 - 0)} = \frac{7}{3}

Hence evaporated water : 10% solution = 7 : 3
If total 3% solution was 50 litres, amount of water evaporated is 35 litres and leftover 10% solution is 15 litres.

dave13 · Answer

KarishmaB thanks. but isnt mean (Aavg) 10% this what confuses me? isnt question saying "to get a 10-percent solution?" so even using this formula, I would mistakenly attribute 10 to Aavg because the question clearly asks for a final solution 10% \frac{w1}{w2} = \frac{(3- 10)}{(10-0)} = - \frac{7}{10}

so I m mixing 3% percent sugar and 0% of water to get 10% sugar concentration , just like here https://gmatclub.com/forum/eight-liters ... s#p3084440 BrentGMATPrepNow maybe you know answer to my question and can explain

KarishmaB · Answer

Think about it: 
Can you mix a 0% sugar solution and 3% sugar solution to get a final 10% sugar solution? 
When one solution is plain water and the other is only 3% sugar, how can you mix them to get 10% solution? The resultant solution will have concentration between 0 and 3% only.

Normally, mixture questions tell us that 0% solution is mixed with 10% solution to give 3% solution. We mix two things. 
Here, our question tells us that a 3% solution is separated into two parts - plain water (0% sugar solution) and a 10% sugar solution. It is the opposite process. We separate a solution into two. We can imagine it in reverse - instead of separating 3% solution into 0% and 10%, we can think that the 3% solution was made by mixing plain water (0% solution) with the 10% solution.

dave13 · Answer

KarishmaB thanks! got it!

How many liters of water must be evaporated from 50 liters of a 3-perc

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