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The ratio, by volume, of baking soda to peroxide to water in

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phoenix9801
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The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   Updated on: 29 Oct 2012, 14:25
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The ratio, by volume, of baking soda to peroxide to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of baking soda to water is halved while the ratio of baking soda to peroxide is doubled. How many cubic centimeters of water will this solution contain if the altered solution will contain 100 cubic centimeters of peroxide?

A. 50
B. 200
C. 400
D. 625
E. 800

The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks.
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E

Originally posted by phoenix9801 on 01 Jun 2012, 11:19.
Last edited by Bunuel on 29 Oct 2012, 14:25, edited 2 times in total.
OA added.
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   02 Jun 2012, 08:00
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phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks.

The ratio, by volume, of baking soda to peroxide to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of baking soda to water is halved while the ratio of baking soda to peroxide is doubled. How many cubic centimeters of water will this solution contain if the altered solution will contain 100 cubic centimeters of peroxide?

A. 50
B. 200
C. 400
D. 625
E. 800


Given: \(\frac{B}{{\frac{P}{W}}}=\frac{2}{{\frac{50}{100}}}\);

The ratio of baking soda to water is halved --> \(\frac{B}{W}=\frac{1}{2}*\frac{2}{100}=\frac{1}{100}=\frac{4}{400}\);

The ratio of baking soda to peroxide is doubled --> \(\frac{B}{P}=2*\frac{2}{50}=\frac{4}{50}\);

New ratio: \(\frac{B}{{\frac{P}{W}}}=\frac{4}{{\frac{50}{400}}}\) --> \(\frac{P}{W}=\frac{50}{400}\) --> if \(P=2*50=100\) then \(W=2*400=800\).

Answer: E.
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Re: Ratio Problem 5 [#permalink] New post   02 Jun 2012, 02:19
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souvik101990 wrote:
Initially
B:P:W=2:50:100
That is B:P=2:50 and B:W=2:100
After altering the solution
B:P is halved i.e B:P now is 1:50
B:W is doubled i.e B:W now is 4:100
So in the new solution B:P:W=4:200:100
That makes P:W=2:1
So water = 50 cc
A is my choice


My working is similar, only thing is probably the ratios are different

B:P:W=2:50:100
That is B:P=2:50 and B:W=2:100
After altering the solution
B:W is halved
New B:w now is 1:100 (or 4:400)
B:P is doubled
New B:P now is 4:50

In new solution
B:P:W = 4:50:400
or 8:100:800

When P is 100cc, Water is 800cc

E, it is.
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Re: Ratio Problem 5 [#permalink] New post   01 Jun 2012, 11:58
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Initially
B:P:W=2:50:100
That is B:P=2:50 and B:W=2:100
After altering the solution
B:P is halved i.e B:P now is 1:50
B:W is doubled i.e B:W now is 4:100
So in the new solution B:P:W=4:200:100
That makes P:W=2:1
So water = 50 cc
A is my choice
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Re: Ratio Problem 5 [#permalink] New post   02 Jun 2012, 02:26
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Oh sorry...
Was posting from the iPad so the question was not available when I was typing the solution..
My bad
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   04 Jun 2012, 12:44
Bunuel wrote:
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks.

The ratio, by volume, of baking soda to peroxide to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of baking soda to water is halved while the ratio of baking soda to peroxide is doubled. How many cubic centimeters of water will this solution contain if the altered solution will contain 100 cubic centimeters of peroxide?

A. 50
B. 200
C. 400
D. 625
E. 800


Given: \(\frac{B}{{\frac{P}{W}}}=\frac{2}{{\frac{50}{100}}}\);

The ratio of baking soda to water is halved --> \(\frac{B}{W}=\frac{1}{2}*\frac{2}{100}=\frac{1}{100}=\frac{4}{400}\);

The ratio of baking soda to peroxide is doubled --> \(\frac{B}{P}=2*\frac{2}{50}=\frac{4}{50}\);

New ratio: \(\frac{B}{{\frac{P}{W}}}=\frac{4}{{\frac{50}{400}}}\) --> \(\frac{P}{W}=\frac{50}{400}\) --> if \(P=2*50=100\) then \(W=2*400=800\).

Answer: E.


Dear Bunuel,
could u pls explain why this "2*50" to P and "2*400" is taken?
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   04 Jun 2012, 12:52
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kashishh wrote:
Bunuel wrote:
phoenix9801 wrote:
The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks.

The ratio, by volume, of baking soda to peroxide to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of baking soda to water is halved while the ratio of baking soda to peroxide is doubled. How many cubic centimeters of water will this solution contain if the altered solution will contain 100 cubic centimeters of peroxide?

A. 50
B. 200
C. 400
D. 625
E. 800


Given: \(\frac{B}{{\frac{P}{W}}}=\frac{2}{{\frac{50}{100}}}\);

The ratio of baking soda to water is halved --> \(\frac{B}{W}=\frac{1}{2}*\frac{2}{100}=\frac{1}{100}=\frac{4}{400}\);

The ratio of baking soda to peroxide is doubled --> \(\frac{B}{P}=2*\frac{2}{50}=\frac{4}{50}\);

New ratio: \(\frac{B}{{\frac{P}{W}}}=\frac{4}{{\frac{50}{400}}}\) --> \(\frac{P}{W}=\frac{50}{400}\) --> if \(P=2*50=100\) then \(W=2*400=800\).

Answer: E.


Dear Bunuel,
could u pls explain why this "2*50" to P and "2*400" is taken?


We have that \(\frac{P}{W}=\frac{50}{400}\) and \(P=100=2*50\). Now, if \(P=100\) then in order \(\frac{P}{W}=\frac{50}{400}\) to hold true W must be 800=2*400.

Or simply: \(\frac{P}{W}=\frac{50}{400}=\frac{100}{800}\).
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   24 Jun 2013, 04:04
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   24 Jun 2013, 05:48
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1. Let the volume of the original solution be v. The ratio of baking soda to peroxide to water is 2:50:100
2. v= 2x+50x+100x
3. The ratio of baking soda to peroxide is doubled and the ratio of baking soda to water is halved.
4 The volume is the same. v= 2y+25y+200y
5. We see if the peroxide is 25 cu.cm, water is 200 cu.cm. If peroxide is 100 cu.cm , water contained is 800 cu.cm
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   04 Jan 2014, 20:58
Ratio to BS/Perox/water = 2/50/100 ; If you halved the ratio of Perox / water =(50/100) *(1/2)= 25/100
At the same time the ratio of BS / Perox is doubled =2/25= 2*(2/50)
Hence the final answer = 2/ 25/100
When perox = 100 = 25*4
Therefore the water = 400

Thanks

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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   19 Apr 2019, 07:26
I took initial ratio given in statement:
S:P:W --> 2:50:100

I altered it based on the info of the statement:
halved S : W --> 2:200
doubled S:P --> 4:50

new ratio is:
S:W:P--> 4:400:50

Extra info: 100l of P (from statement)
Thus: 50x=100 --> x=2
Use x=2 to find liters of water in the solution. 400*2=800l of water

:)

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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink] New post   21 Jul 2023, 23:23
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Re: The ratio, by volume, of baking soda to peroxide to water in [#permalink]
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