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# Papayaya, a popular soft drink, contains only four ingredien

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Papayaya, a popular soft drink, contains only four ingredien [#permalink]  12 Jul 2012, 07:55
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Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?

A. 7/30
B. 7/21
C. 2/5
D. 12/29
E. 4/7

How to attack these problems other than plugging-in numbers?
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Jul 2012, 11:44, edited 1 time in total.
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Re: Papayaya, a popular soft drink, contains only four ingredien [#permalink]  12 Jul 2012, 10:31
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Find the ratios of the mixed quantities first by standardizing the denominator. There are 4 ingredients with Soda water = 4/7 and natural lemon juice = 1/3 of Papayaya. The common denominator will be 7 * 3 = 21. Thus, quantities will be:

Soda water = 12/21
Natural lemon juice = 7/21

The quantities of sugar and papaya puree are equal. Total units are 21 of which 12 + 7 = 19 are used up by above two. Remaining is 2 which is equally divided between sugar and papaya puree:

Sugar = 1/21
Papaya puree = 1/21

Thus ratio of soda:lemon:sugar:puree = 12:7:1:1

Now, lemon is doubled, puree is three times and remaining are the same.
Resultant ratio is = 12:14:1:3

Ratio of soda water in the resultant mixture = 12/(12+14+1+3) = 12/30 = 2/5
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Re: Papayaya, a popular soft drink, contains only four ingredien [#permalink]  12 Jul 2012, 12:01
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superpus07 wrote:
Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?

A. 7/30
B. 7/21
C. 2/5
D. 12/29
E. 4/7

How to attack these problems other than plugging-in numbers?

Given that Papayaya contains:
$$\frac{4}{7}=\frac{12}{21}$$ of soda water;

$$\frac{1}{3}=\frac{7}{21}$$ of lemon juice;

$$\frac{1}{21}$$ of sugar: $$\frac{1-(\frac{12}{21}+\frac{7}{21})}{2}$$;

$$\frac{1}{21}$$ of papaya puree: $$\frac{1-(\frac{12}{21}+\frac{7}{21})}{2}$$.

So, out of total of 21 units we need 12 units of soda water, 7 units of lemon juice, 1 unit of sugar and 1 unit of papaya puree.

Due to a malfunction, the mixing machine used 7*2=14 units of lemon juice (instead of 7) and 1*3=3 units of papaya puree (instead of 1).

Hence, the fraction of soda water in the final mixture is $$\frac{12}{12+14+3+1}=\frac{12}{30}=\frac{2}{5}$$.

Hope it helps.
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Joined: 13 Feb 2010
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Re: Papayaya, a popular soft drink, contains only four ingredien [#permalink]  26 Jul 2012, 20:12
[quote="Edvento"]Find the ratios of the mixed quantities first by standardizing the denominator. There are 4 ingredients with Soda water = 4/7 and natural lemon juice = 1/3 of Papayaya. The common denominator will be 7 * 3 = 21. Thus, quantities will be:

Soda water = 12/21
Natural lemon juice = 7/21

The quantities of sugar and papaya puree are equal. Total units are 21 of which 12 + 7 = 19 are used up by above two. Remaining is 2 which is equally divided between sugar and papaya puree:

Sugar = 1/21
Papaya puree = 1/21

Thus ratio of soda:lemon:sugar:puree = 12:7:1:1

Now, lemon is doubled, puree is three times and remaining are the same.
Resultant ratio is = 12:14:1:3

Hey, your method looks very simple.Does taking the common denominator work well always.
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Re: Papayaya, a popular soft drink, contains only four ingredien [#permalink]  18 Apr 2014, 23:18
Soda: 4/7

LJ: 1/3

S: 1/21

PP: 1/21

Due to malfunctioning:

Soda remains as it is

LJ: 2/3

PP: 3/21

Hence the proportion of Soda in solution

{4/7}/ {4/7 + 2/3+ 1/21 + 3/21}

2/5
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Re: Papayaya, a popular soft drink, contains only four ingredien   [#permalink] 18 Apr 2014, 23:18
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