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Mixture sum 2

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by [email protected] » Wed Jun 08, 2011 6:49 am
Two vessels A and B contain milk and water mixed in the ratio 5:2 and 8:5 respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing milk and water in the ratio 9:4.

A] 5:2
B] 3:4
C] 2:5
D] 7:2
E] 2:9


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by cans » Wed Jun 08, 2011 6:55 am
A: m:w = 5:2
B: m:w=8:5
let ration is 7x:13 (a:b)
total milk = 5x+8
total water = 2x+5
(5x+8)/(2x+5) = 9:4
20x+32 = 18x+45
x=13:2
thus ratio = (7/13)*(13:2)
=7:2
IMO D
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by GMATGuruNY » Wed Jun 08, 2011 7:14 am
[email protected] wrote:Two vessels A and B contain milk and water mixed in the ratio 5:2 and 8:5 respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing milk and water in the ratio 9:4.

A] 5:2
B] 3:4
C] 2:5
D] 7:2
E] 2:9


OA later...
Fraction of milk in A = 5/7 = 65/91.
Fraction of milk in B = 8/13 = 56/91.
Fraction of milk in mixture = 9/13 = 63/91.

Using alligation:

The proportion needed of each element in the mixture is equal to the distance between the fraction attributed to the other element and the fraction attributed to the mixture.

Proportion of A in the mixture = 63/91 - 56/91 = 7/91.
Proportion of B in the mixture = 65/91 - 63/91 = 2/91.
Ratio of A to B in the mixture = 7/91 : 2/91 = 7:2.

The correct answer is D.
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by iamsaurav » Wed Jun 08, 2011 7:39 am
Please explain your reasoning I am not able to follow it, you have added the ratios, why?
cans wrote:A: m:w = 5:2
B: m:w=8:5
let ration is 7x:13 (a:b)
total milk = 5x+8
total water = 2x+5
(5x+8)/(2x+5) = 9:4
20x+32 = 18x+45
x=13:2
thus ratio = (7/13)*(13:2)
=7:2
IMO D
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by TuanNguyen87 » Wed Jun 08, 2011 2:27 pm
GMATGuruNY wrote:
[email protected] wrote:Two vessels A and B contain milk and water mixed in the ratio 5:2 and 8:5 respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing milk and water in the ratio 9:4.

A] 5:2
B] 3:4
C] 2:5
D] 7:2
E] 2:9


OA later...
Fraction of milk in A = 5/7 = 65/91.
Fraction of milk in B = 8/13 = 56/91.
Fraction of milk in mixture = 9/13 = 63/91.

Using alligation:

The proportion needed of each element in the mixture is equal to the distance between the fraction attributed to the other element and the fraction attributed to the mixture.

Proportion of A in the mixture = 63/91 - 56/91 = 7/91.
Proportion of B in the mixture = 65/91 - 63/91 = 2/91.
Ratio of A to B in the mixture = 7/91 : 2/91 = 7:2.

The correct answer is D.
Excuse me Mr GuruNy,

But i think the Proportion of A in the mixture is supposed to = 63/91 - 65/91, and Proportion of B in the mixture is supposed to = 63/91 - 56/91, instead of Proportion of A in the mixture = 63/91 - 56/91, and Proportion of B in the mixture = 65/91 - 63/91? Is it right? Please explain help me because I like your solution method.

Thanks so much!
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by cans » Wed Jun 08, 2011 8:00 pm
iamsaurav wrote:Please explain your reasoning I am not able to follow it, you have added the ratios, why?
cans wrote:A: m:w = 5:2
B: m:w=8:5
let ration is 7x:13 (a:b)
total milk = 5x+8
total water = 2x+5
(5x+8)/(2x+5) = 9:4
20x+32 = 18x+45
x=13:2
thus ratio = (7/13)*(13:2)
=7:2
IMO D
I assumed we took 7x portion of A and 13 portion of B
Thus milk from portion A = (5/7)(7x) = 5x
milk form portion B = (8/13)(13)=8
Thus total milk in mixture = milk from A + milk from B = 5x+8
Similarly total water in mixture = 2x+5
given milk:water in mixture=9:4
Thus (5x+8)/(2x+5)=9:4
Solve for x. and then find the asked ration = 7x:13
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by bubbliiiiiiii » Thu Jun 09, 2011 1:12 am
Hi Mitch,

How did you deduce this?
Fraction of milk in mixture = 9/13 = 63/91.
Regards,

Pranay
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by Frankenstein » Thu Jun 09, 2011 1:17 am
bubbliiiiiiii wrote:Hi Mitch,

How did you deduce this?
Fraction of milk in mixture = 9/13 = 63/91.
Hi,
a new mixture containing milk and water in the ratio 9:4.

So, Fraction of milk in mixture = 9/(9+4) = 9/13 = 9*7/(13*7) = 63/91 just to make the denominator same for all the 3 values.
Cheers!

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by greaborade » Fri Sep 04, 2015 11:18 am
why u to take 7x only i checked its not correct when we use 13x??
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by Matt@VeritasPrep » Fri Sep 04, 2015 5:12 pm
greaborade wrote:why u to take 7x only i checked its not correct when we use 13x??
It has to do with the sums of each ratio. A has a ratio of 5:2, which sums to (5+2), or 7; B has a ratio of 8:5, which sums to (8+5), or 13.
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