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Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 63% (02:14) correct 37% (02:34) wrong based on 202 sessions

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Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 1:3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1?

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

Source: Aristotle.

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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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3
Container 1:
Let each part be x.
Vol of A= 5x ; Vol of B= x ; Total Vol= 6x.

Container 2:
Let each part be y.
Vol of A= y ; Vol of B= 3y; Total Vol= 4y.

After Mixing:
Vol of A= 5x + y
Vol of B= x + 3y
As Ratio of A:B is 1:1, hence
5x+y = x+3y
2x = y
So,
Ratio of Total Vol 1 : Total Vol 2 =
6x / 4y = 6x / 4(2x) = 6/8 = 3/4.
Hence, Ans is Option D
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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Let's say X amount of Liquid in container 1 is mixed with Y amount of Liquid in container 2

so

$$\frac{5x}{6}$$ + $$\frac{y}{4}$$= $$\frac{x + y}{2}$$

4x = 3y

$$\frac{x}{y}$$ = $$\frac{3}{4}$$
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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Gnpth wrote:
Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 1:3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1?

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

Source: Aristotle.

Lets assume the same quantity of the liquid in both the containers : 12 units.
Container 1 contains 10 units of liquid A and 2 units of liquid B
Container 2 contains 3 units of liquid A and 9 units of liquid B

Since the liquid in both the containers need to be mixed, such that the resulting
liquid has a ratio of 1:1(unit of liquid A : unit of liquid B)

Since the concentration of Liquid A must be equal to concentration of Liquid B
from both the containers.
$$10x + 3y = 2x + 9y$$
$$8x = 6y$$
$$\frac{x}{y} = \frac{3}{4}$$(Option D)
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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Gnpth wrote:
Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 1:3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1?

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

Source: Aristotle.

A in container 1 represents 5/6 of its entire content. In the same way, A represents 1/4 of the content of container 2.

Now we want both A and B to represent each 1/2 of the new container (let's call it H).

So, for container 1 let's call the proportion of liquid A "x" and "y" for the other container, being y = 1 - x

We'll have: 5/6*x + 1/4*(1-x) = 1/2

If you solve it, you'll get: x = 3/7.

This means that liquid A from container 1 will occupy 3/7 of the total amount of liquid A in H. Liquid A from container 2 will occupy 4/7.

The same will happen with liquid B (1/2 * 3/7 + 3/4 * 4/7 = 1/2).

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Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Let the quantity of container 1 be x and container 2 be y
Then quantity of A in container 1 =5/6*X
Quantity of A in container 2= 1/4*x
Now we are given that the ratio of these two liquids in mixture is 1:1
Now we can set up the equation as
5/6*x +1/4*y =1/2(x+y)
20x+6y=24/2(x+y)
8x=6y
x/y=3/4
Hence D

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Posts: 20
Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the  [#permalink]

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Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 1:3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1?

shortest method

Container 1, proportion of A = 5/6
Container 2, proportion of A = 1/4
Total proportion of A once Container 1 and 2 are mixed = 1/2

Weighted avg of W1/W2 = (1/4 - 1/2) / (1/2 - 5/6) = 3/4

So the contents of both containers should be mixed in the proportion 3:4 in order to reach the desired total ratio

IMO: D

cheeeers  Re: Two liquids A and B are in the ratio 5:1 in container 1 and in the   [#permalink] 19 Apr 2019, 09:45
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