Word problem

[grems]

After 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution went down by one-third. How much of the 24%-solution was used?

A) 180
B) 220
C) 250
D)350
E)400

[amit_ace]

E

(24%*400)/600=16%

[CallMeDaOne]

Let the total weight of the 24% solution used is x gms.
Then weight of alcohol in the 24% solution = 0.24x gms

After the addition of 200gm of water, the strength becomes,

(0.24x)/(x+200).

The new strength is given as 16%. So we get,

(0.24x)/(x+200) = 0.16
=>0.24x = 0.16(x+200)
=>3x = 2(x+200)
=>3x - 2x = 400
=> x = 400.

So the answer is E

Regards.

[grems]

Where does the 16% come from?

I had the equation set up properly but got thrown off by what the right side of the equation should look like.

[Fiver]

I didn't quite get what value the question is looking for. It its looking for how many grams is 16 % of the solution it is 400.
As 8% solution -200 grams water
16% solutoin - 400 grams water

Hence E

[NishantG]

E for me too

[nikhilsikri]

E here

[CallMeDaOne]

The question says "the strength of the solution went down by one-third".

The original strength of the solution is given as 24%.
One third of 24% is 8%. So the new strength of the solution is 24-8 = 16%.

Hope that helps.

Regards.

Originally Posted by grems

Where does the 16% come from?

I had the equation set up properly but got thrown off by what the right side of the equation should look like.

[btit]

How much of the 24%-solution was used?

what does this mean?? I am not getting what que is asking really?

1/3 of 24% is 8%.
So, 8% =>200 gms, then 16% => 400gms..

I dont think que is asking this simple.., do you?

[Anson800]

24161608
=> 8/24(200+x)=200=>x=400