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# In what ratio should a mixture of milk and water in the

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In what ratio should a mixture of milk and water in the  [#permalink]

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25 Aug 2014, 07:01
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In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

Source : 4gmat
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Joined: 02 Sep 2009
Posts: 49915
Re: In what ratio should a mixture of milk and water in the  [#permalink]

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25 Aug 2014, 07:11
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alphonsa wrote:
In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

Source : 4gmat

First mixture: milk and water in the ratio of 3x:4x.
Second mixture: milk and water in the ratio 5y:2y.

We want their mixture to have equal quantities of milk and water: 3x + 5y = 4x + 2y --> x/y = 3.

For example, if we have 21 gallons of mixture 1 (9 gallons of milk and 12 gallons of water), then we need to mix it with 7 gallons of mixture 2 (5 gallons of milk and 2 gallons of water) in order to get a new 28-gallon mixture with 14 gallons of milk and 14 gallons of water.

Hope it's clear.
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Re: In what ratio should a mixture of milk and water in the  [#permalink]

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08 Mar 2016, 03:06
3
alphonsa wrote:
In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

Source : 4gmat

Weighted Average and Mixture Problems on the GMAT
Mixture Tips and Tricks

DS Mixture Problems
PS Mixture Problems

Hope it helps.
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Re: In what ratio should a mixture of milk and water in the  [#permalink]

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11 Mar 2016, 01:54
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alphonsa wrote:
In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

Source : 4gmat

Responding to a pm:

Here is how you can use the weighted average formula: Focus on one element only say milk. Milk concentration is 3/7 in first mix and 5/7 in the second mix.

w1/w2 = (A2 – Aavg)/(Aavg – A1)

$$\frac{w1}{w2} = \frac{5/7 - 1/2}{1/2 - 3/7}$$

$$\frac{w1}{w2} = \frac{3}{1}$$

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In what ratio should a mixture of milk and water in the  [#permalink]

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11 Mar 2016, 21:55
3x/7+5y/7=3.5(x+y)/7
x/y=3
x:y=3:1
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Re: In what ratio should a mixture of milk and water in the  [#permalink]

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13 Mar 2016, 08:58
alphonsa wrote:
In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

Source : 4gmat

You can solve this problem in two ways. I use here the second method which is easier to type.
Supposing that the first mixture has 3*x milk and 4*x water and the second mixture has 5*y milk and 2*y water.
By supposition, 3*x +5*y = 4*x + 2*y
Solving, we get x to y is 3 to 1.
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Re: In what ratio should a mixture of milk and water in the  [#permalink]

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06 Apr 2017, 09:48
alphonsa wrote:
In what ratio should a mixture of milk and water in the ratio of 3:4 be mixed with another mixture of milk and water in the ratio 5:2 so that the resultant mixture contains equal quantities of milk and water?

A) 3:1
B) 3:5
C) 7:8
D) 7:9
E) 9:11

We can let the ratio of milk to water in the first mixture be 3x : 4x in which 3x and 4x are the weights of the milk and water, respectively. (Notice the weight of the first mixture will be 3x + 4x = 7x.)

Similarly, we can let the ratio of milk to water in the second mixture be 5y : 2y in which 5y and 2y are the weights of the milk and water, respectively. (Notice the weight of the second mixture will be 5y + 2y = 7y.)

Thus we need:

3x + 5y = 4x + 2y

3y = x

Since x = 3y, the weight of the first mixture is 7x = 7(3y) = 21y. Thus, the ratio in weight of the first mixture to the second mixture is 21y : 7y = 3 : 1.

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Re: In what ratio should a mixture of milk and water in the  [#permalink]

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16 Oct 2017, 09:43
There are two equations here, either of which, when solved, will give the correct answer.

1) $$(\frac{3}{7})*X+(\frac{5}{7})*Y = (\frac{1}{2})*(X+Y)$$

2) $$(\frac{4}{7})*X+(\frac{2}{7})*Y = (\frac{1}{2})*(X+Y)$$

A common mistake is to take RHS as (X+Y) instead of $$(\frac{1}{2})*(X+Y)$$

The ratio $$\frac{x}{y} = \frac{3}{1}$$
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Re: In what ratio should a mixture of milk and water in the &nbs [#permalink] 16 Oct 2017, 09:43
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