M21-21

Question

After 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third. What was the weight of the original 24% solution ?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

Bunuel · Accepted Answer

Official Solution:

After 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third. What was the weight of the original 24% solution ?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

Let the weight of the 24% solution be  x  grams, then the weight of alcohol in it would be  0.24x  grams. Next, since in the final solution the strength decreased by  \frac{1}{3} , then the strength of the final solution is  24*\frac{2}{3}=16 \% .
 
Since the amount of alcohol in the original and the final solutions is the same, we can equate them and set the equation:  0.24x=0.16(x+200) .
 
Solving gives:  x=400 .

Answer: E

mvictor · Answer

I solved it a little bit different, and I don't know whether I was lucky to get the right answer or not.
we had 0.24x = alcohol and 0.76x = water.
We have added 200 grams of water, and therefore have x+200 - total volume
we know that the concentration of alcohol has decreased by 1/3 => which means we have 16% alcohol in new solution
0.16(x+200) + 0.76x+200 = x+200
we then have:
0.92x +32 = x
32 = 0.08x
x = (32 * 100) / 8
x = 400

but I guess my method is more lengthy.

nickimonckom · Answer

Hi I use a different method and solve it really quickly :

After the water has been added the concentration decrease by  \frac{1}{3} .

It means that  \frac{1}{3}  of the final mixture contains no alcohol and therefore is water.

Hence, 200g of water =  \frac{1}{3}  of final mixture

Final Mixture  = 600g wich 200g are water and 400 are the initial solution

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

adityakaregamba · Answer

how did you infer that the amount of alcohol in the original and the final solution is same? 
 Bunuel

Bunuel · Answer

Adding water, which has no alcohol, to an alcohol solution will not increase the amount of alcohol in the final solution.

Sushi_545 · Answer

HI  Bunuel ,

Now I am actually confused strength of the solution decreased by one-third I inferred it as 1/3 of the original solution and not 1-1/3 I have seen many questions here which use the same logic which I have used how come here you are taking it as 1-1/3 here?

Bunuel · Answer

“Decreased by one-third” means you take away one-third of the original amount, so what’s left is the other two-thirds of the original. Or consider it this way: decreased by 1/3 is the same as decreased by about 33%.

Sushi_545 · Answer

Hi  Bunuel ,

I do understand what you are trying to say buy i have seen many question previously on gmat club itself where deacreased by one third is taken as a factor of 1/3 only and not 1-1/3.

Why here it is done so?

Bunuel · Answer

Show those other questions.

M21-21

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