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 : 14
B. 27 : 13
C. 27 : 16
D. 27 : 18
E. 27 : 17

Are You Up For the Challenge: 700 Level Questions

A. 27 : 14
B. 27 : 13
C. 27 : 16
D. 27 : 18
E. 27 : 17

Are You Up For the Challenge: 700 Level Questions

Nidzo · Answer

Bottle 1 water: \frac{2}{9}
Bottle 2 water: \frac{4}{13}
Mixed bottle water: \frac{1}{4}

Using Alligation:

\frac{2}{9} ....................  \frac{4}{13} 
............. \frac{1}{4} ............
(1)..........................(2)

(1)
 \frac{1}{4}-\frac{2}{9} 
 \frac{9}{36} - \frac{8}{36} 
 \frac{1}{36}

(2)
 \frac{4}{13} - \frac{1}{4} 
 \frac{16}{52}-\frac{13}{52} 
 \frac{3}{52}

Ratios:  \frac{1}{36}:\frac{3}{52} 
 \frac{1}{36}*\frac{52}{3} 
 \frac{52}{108} 
 \frac{13}{27} 
 13:27

Answer B

Loulou75 · Answer

I use the distance trick:

2/9 ------- 1/4 --------- 4/13

2/9 - 1/4 = 1/36
4/13- 1/4 = 3/52

thus the final ratio is 3/52 / 1/36 = 27/13

Krunaal · Answer

One way to go about this is, since you see 27 in answer choices, and bottle 1 is 7:2 => 7x + 2x => 9x; multiplying 7:2 by 3 => 21:6

You can also see 13, in option (B), and bottle 2 is 9:4 => 9x + 4x => 13x; so we keep 9:4 as is.

Now mixing bottle 1 and bottle 2 => 21 + 9 : 6 + 4 => 30:10 =>  3:1

You get milk and water in 3:1 ratio, so  27:13  is the correct answer.

Navdeep2000 · Answer

Let's assume Bottle 1 has 9x amount of solution, i.e. 7x of milk and 2x of water as per the given. 
 Likewise, let's assume Bottle 2 has 13y amount of solution, i.e. 9y of milk and 4y of water.

Now, as our next step, we are told that the new ratio obtained should be 3:1.

If we put this in work, we are told that the ratio of milk in the overall solution should be:
(7x+9y)/(9x+13y)=3/4 
or (28x + 36y) = (27x + 39y)

Finally, it's x=3y

Plugging in the value of x in our combined solutions of Bottle 1 and 2 would get us = 9x:13y or 9(3y):13y = 27:13.   Option B

(Note: In mixture questions, going by a diagram in your rough work really helps to understand better and solve efficiently)

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

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

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