Solution

Given
In this question, we are given that

• Bottle 1 contains a mixture of milk and water in 7: 2 ratio and Bottle 2 contains a mixture of milk and water in 9: 4 ratios

To find
We need to determine

• The ratio of volumes, in which the liquids in Bottle 1 and Bottle 2 should be combined to obtain a mixture of milk and water in 3: 1 ratio

Approach and Working
Let us assume that volume of mixture in bottle 1 is x and volume of mixture in bottle 2 is y, that is to be mixed

• Amount of milk in the respective bottles = 7x/9 and 9y/13
• Amount of water in the respective bottles = 2x/9 and 4y/13

As per the question given,

• (7x/9 + 9y/13)/(2x/9 + 4y/13) = 3/1
Simplifying, we get x/y = 27/13

Thus, option A is the correct answer.

Correct Answer: Option A
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w1/w2=(A2–Aavg)/(Aavg–A1)
here, A2 = 9/(9+4) , A1 = 7/(7+2) , Aavg = 3/(3+1) [ Considering milk, one can consider water also ]
w1/w2 = 27/13

correct answer is A

Let us equate only the Milk from the mixture. Let us assume the bottles are mixed in A:B ratio.

Bottle 1 has milk in 7/9 ratio. Bottle 2 has milk in 9/13 ratio. And the total milk = 3/4 ratio.

=> (7/9)*(A/[A+B]) + (9/13)*(B/[A+B]) = 3/4

By solving that, we get 13A = 27B

=> A/B = 27/13

Ans A

By the theory of compound mixtures, when V1 Volume/Quantity of a mixture of X and Y which is in the ratio a : b is mixed with V2 Volume/Quantity of another mixture X and Y (i.e the constituents of the 2 mixtures are the same in the ratio p : q, then the final ratio of the constituents is given by

\(\frac{X}{Y}\) = \(\frac{X from V_1 + X from V_2 }{Y from V_1 + Y from V_2} = \frac{(\frac{a}{a + b})*V_1 + (\frac{p}{p + q})*V_2}{(\frac{b}{a + b})*V_1 + (\frac{q}{p + q})*V_2}\)

In the question above, we have to find the ratio of volumes, \(\frac{V_1 }{ V_2}\)


Total amount of Milk from the 2 containers = \(\frac{7}{7 + 2} * V_1 + \frac{9}{9 + 4} * V_2 = \frac{7}{9} * V_1 + \frac{9}{13} * V_2\)

Total amount of water from the 2 containers = \(\frac{2}{7 + 2} * V_1 + \frac{4}{9 + 4} * V_2 = \frac{2}{9} * V_1 + \frac{4}{13} * V_2\)

Ratio of \(\frac{M}{W}\) = \(\frac{3}{1}\) = \( \frac{(\frac{7}{9})*V_1 + (\frac{9}{13})*V_2}{(\frac{2}{9})*V_1 + (\frac{4}{13})*V_2}\) = \(\frac{\frac{91 V_1 + 81 V_2}{117}}{\frac{26 V_1 + 36 V_2}{117}} = \frac{91 V_1 + 81 V_2}{26 V_1 + 36 V_2}\)

Cross Multiplying, we get \(78 V_1 + 108 V_2 = 91 V_1 + 81 V_2\)

\(27 V_2 = 13 V_1\)

\(\frac{V_1}{V_2} = \frac{27}{13}\)

\(V_1 : V_2 = 27 : 13\)

Option A

Arun Kumar
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The simplest way can be through alligation.

Let's take the ratio of milk throughout

..7/9 .... 9/13

.......3/4

..3/52 .... 1/36

=> 108 : 52
=> 54 : 26
=> 27 : 13

So Option A

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