Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottl

Question

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 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

A. 27 : 13
B. 27 : 14
C. 27 : 16
D. 27 : 18
E. 27 : 19

Show Answer

Official Answer

A

A. 27 : 13
B. 27 : 14
C. 27 : 16
D. 27 : 18
E. 27 : 19

EgmatQuantExpert · Accepted Answer

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

Shreyaag13 · Answer

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

preetamsaha · Answer

w1/w2=(A2–Aavg)/(Aavg–A1)
here, A2 = 9/(9+4) , A1 = 7/(7+2) , Aavg = 3/(3+1)  
w1/w2 = 27/13

correct answer is A

TheGuyDangerous · Answer

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/ ) + (9/13)*(B/ ) = 3/4

By solving that, we get 13A = 27B

=> A/B = 27/13

Ans A

CrackverbalGMAT · Answer

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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Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottl

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