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Two jars P and Q contain the same quantity of a mixture of milk and

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Q51  V47
Re: Two jars P and Q contain the same quantity of a mixture of milk and [#permalink]
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bv8562 wrote:
IanStewart Could you please share the best way to solve this question?

Alligation is the best method for any similar problem. Not sure if you're familiar with that method, but I don't have time to explain it in full detail, so this solution might seem a bit mysterious (though from this one solution alone, you may be able to abstract the important principles, and you can read about it elsewhere). We're mixing one thing that is 5/7 milk with another that is 4/5 milk, and getting a mixture that is 3/4 milk. Getting common denominators, we're mixing 100/140 milk with 112/140 milk and getting 105/140 milk. Once the denominators are the same, we can just ignore them (though there's no harm in keeping them around if you want to) -- we can now just draw these three numbers on a number line:

---100-----105---------112----

and by alligation principles, the ratio of the two distances to the middle must be equal to the ratio in which we're mixing the two components. The two distances to the middle are 105-100 = 5 and 112-105 = 7, so we're mixing the two parts in a 5 to 7 ratio, and since 105 is closer to 100, we're using more of the 100/140 = 5/7 component, which is P, so the ratio of P to Q is 7 to 5.

You'd probably need to resort to algebra if you didn't know alligation. If we have p litres of P, then since P is 5/7 milk, we get (5/7)p litres of milk from P. Similarly we get (4/5)q litres of milk from Q. Overall we have p+q litres of mixture, and it's 3/4 milk, so overall we have (3/4)(p + q) litres of milk. So

(5/7)p + (4/5)q = (3/4)(p + q)
(4/5 - 3/4)q = (3/4 - 5/7)p
(1/20)q = (1/28)p
p/q = 28/20 = 7/5

but for many reasons, this is an approach I really dislike for GMAT purposes.
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Two jars P and Q contain the same quantity of a mixture of milk and [#permalink]
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Bunuel wrote:
Two jars P and Q contain the same quantity of a mixture of milk and water. The milk and water in P and Q are in the ratio 5 : 2 and 4 : 1 respectively. What will be the ratio in which these two mixtures have to be blended to obtain a new mixture of milk and water in the ratio of 3 : 1?

(A) 5 : 6
(B) 1 : 1
(C) 4 : 3
(D) 7 : 5
(E) 3 : 2

We will work with the concentration of one of the ingredients - say milk

$$\frac{w1}{w2} =\frac{ (A2 - Avg)}{(Avg - A1)}$$

$$\frac{w1}{w2} =\frac{(4/5 - 3/4)}{(3/4 - 5/7)}$$

$$\frac{w1}{w2} =\frac {(1/20)}{(1/28)}$$

$$\frac{w1}{w2} =\frac{ 7}{5}$$