How much pure alcohol should be added to 400 ml of a 15% solution to

Question

How much pure alcohol should be added to 400 ml of a 15% solution to make the strength of the solution 32%?

(A) 80ml
(B) 100 ml
(C) 120 ml
(D) 150 ml
(E) 160 ml

chetan2u · Answer

Alcohol in 400 ml of 15% solution =  400*\frac{15}{100}=60 , and water = 400-60=340.
There is no change in the 340ml, and it becomes 100-32 or 68% in the new solution of say x ml.

340=\frac{68}{100}*x 
 x=340*\frac{100}{68}=500ml 
The alcohol added = 500-400=100ml.

OR

Only alcohol gets added, say y ml.
Then  \frac{60+y}{400+y}=\frac{32}{100} 
 100(60+y)=32(400+y) 
 6000+100y=12800+32y 
 68y=6800 
 y=100

B

GMATinsight · Answer

Answer: Option B Video solution by GMATinsight https://www.youtube.com/watch?v=G0hD_04TfB0 Screenshot 2021-03-06 at 1.27.47 PM.png

Kinshook · Answer

Asked: How much pure alcohol should be added to 400 ml of a 15% solution to make the strength of the solution 32%?

In 400 ml solution:
Alcohol = 60 ml

Let x ml of Pure alcohol be added to the solution to make the strength of the solution 32%
(60 + x)/(400+x) = .32
60 + x = 128 + .32x
.68x = 68
x = 100 ml

IMO B

argerniki · Answer

Testing some of the answers was the fastest way in my opinion.
I always start with either B or D and then move up-/downwards based on the result (if necessary).

Say I start with (D) 150 ml:

First of all, how much pure alc contains the solution at the beginning?
400 * 15% = 60 ml

In other terms, you can say that the concentration = volume of the solute / total volume

Now lets add 150 ml to the solution and check its concentration:
volume of solute / total volume =  \frac{(60 + 150)}{(400 + 150)} = \frac{210}{550} = \frac{21}{55}  which is slightly less than  \frac{2}{5} , therefore slightly less than  \frac{40}{100} =   40%

This  concentration is too high , therefore I need to  add less alcohol .

Let's check answer (B) 100 ml:

\frac{(60 + 100)}{(400 + 100)} = \frac{160}{500} = \frac{16}{50} = \frac{32}{100} =   32%

That's the correct solution,  Answer B 
Notice that this was the slower option: if you had picked B right away, you were done after 1 calculation.

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How much pure alcohol should be added to 400 ml of a 15% solution to

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How much pure alcohol should be added to 400 ml of a 15% solution to

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