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

Answer = A) 35


Sugar should constitute 10% of the solution post water removal
\(\frac{10}{100} (50-x) = 1.5\)

x = 50-15 = 35

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

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.

Hi Paresh. Thanks for the reply.

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

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.

Hi Paresh. Thanks for the reply.

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

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.

Tough and Tricky questions: Mixture Problems.

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

Kudos for a correct solution.

Source: Chili Hot GMAT

Tough and Tricky questions: Mixture Problems.

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

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

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 ?

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.

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

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.