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Manager  B
Joined: 23 Nov 2014
Posts: 60
Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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16 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:30) correct 32% (02:57) wrong based on 219 sessions

### HideShow timer Statistics Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

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

Originally posted by ruchi857 on 14 May 2016, 09:11.
Last edited by Bunuel on 15 Mar 2019, 03:43, edited 2 times in total.
Edited the question.
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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ruchi857 wrote:
Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

A) 2:7
B) 5:2
C) 3:5
D) 5:7

Hi,
say A qty of vessel A and B qty of vessel B is added together..
Lets concentrate on quantity of milk

$$\frac{8A}{13}+ \frac{5B}{7}= \frac{9}{13}(A+B)$$ ...

$$\frac{8A}{13}+ \frac{5B}{7}= \frac{9A}{13}+\frac{9B}{13})$$ ..

$$\frac{5B}{7}-\frac{9B}{13}=\frac{9A}{13}-8A/13$$.....

$$\frac{65B-63B}{7*13}=\frac{A}{13}$$...

$$\frac{2B}{7*13}=\frac{A}{13}$$....

$$\frac{A}{B}=\frac{2}{7}$$

A
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Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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3
2
Another method:

Required Ratio = $$\frac{\frac{5}{7} - \frac{9}{13}}{\frac{9}{13} - \frac{8}{13}}$$ = $$\frac{2}{7}$$

##### General Discussion
Manager  B
Joined: 16 Jan 2013
Posts: 79
GMAT 1: 490 Q41 V18 GMAT 2: 610 Q45 V28 GPA: 2.75
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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1
Not sure what’s wrong with the following approach:

In vessel A: milk = 8x, water = 5x
In vessel B: milk = 5y, water = 2y
According to the question stem 8x + 5y : 5x + 2y should equal to 9:4

Hence, 8x + 5y / 5x + 2y = 9/4
=> 2y = 13x
=> x/y = 2/13 Regards.
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Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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4
3
Not sure what’s wrong with the following approach:

In vessel A: milk = 8x, water = 5x
In vessel B: milk = 5y, water = 2y
According to the question stem 8x + 5y : 5x + 2y should equal to 9:4

Hence, 8x + 5y / 5x + 2y = 9/4
=> 2y = 13x
=> x/y = 2/13 Regards.

Hi,

you have started well but left it in between....

it is fine till
$$\frac{x}{y} = \frac{2}{13}$$.....
But we are not looking for x/y..
what is the total of FIRST mixture = 8x+5x = 13x....
and SECOND mix = 5y+2y = 7y...

so we are looking for $$\frac{13x}{7y}$$......
$$\frac{x}{y}= \frac{2}{13}$$, so$$\frac{x}{y}*\frac{13}{7} = \frac{2}{13}*\frac{13}{7}.......... \frac{13x}{7y} = \frac{2}{7}$$....
ans$$\frac{2}{7}$$
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Posts: 1206
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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1
8A/13+5B/7=9/13(A+B)
A/B=2/7
A:B=2:7
Manager  S
Joined: 22 Nov 2016
Posts: 205
Location: United States
GPA: 3.4
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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1
There are two equations here, either one of which, when solved, will get you the final answer.

1) $$(\frac{8}{13})*X + (\frac{5}{7})*Y = (\frac{9}{13})*(X+Y)$$

2) $$(\frac{5}{13})*X + (\frac{2}{7})*Y = (\frac{4}{13})*(X+Y)$$

Both equations lead to$$\frac{X}{Y} = \frac{2}{7}$$
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Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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1
In questions like this concentrate only on one of the ingredients of the mixture.

Let us take milk.

what is the percentage of milk in A=8/13. (When we have a ratio like given in this question 8:5 add them to get the total)

% of milk in B=5/7

% of milk after mixing=9/13=average after mixing 2 solutions or mixtures.

use weighted average formula

w1/w2=(A2-avg)/(avg-A1). Here A1=A and A2=B

A1=8/13, A2=5/7 and Avg=9/13. (You can take A1 and A2 as any of the given value and you will get the same answer)

w1/w2=(5/7-9/13)÷(9/13-8/13)=[(65-63)/91]÷[(9-8)/13]=2/91÷1/13=2/7 or 2:7 answer is =A
Intern  Joined: 23 Mar 2018
Posts: 1
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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8/13 5/7
\
\
9/13
\
\
2/91 1/13

=2/91:1/13= 2/91*13/1

Posted from my mobile device
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Posts: 2823
Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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ruchi857 wrote:
Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

A) 2:7
B) 5:2
C) 3:5
D) 5:7

We can create the ratios:

Vessel A:

milk : water = 8x : 5x and so 8x + 5x = 13x (Eq. 1)

Vessel B:

milk : water = 5y : 2y and so 5y + 2y = 7y (Eq. 2)

We can create the equation:

(8x + 5y)/(5x + 2y) = 9/4

4(8x + 5y) = 9(5x + 2y)

32x + 20y = 45x + 18y

2y = 13x (Eq. 3)

Notice that Eq. 1 stated that 8x + 5x = 13x; thus, in terms of y, we use Eq. 3 to state that vessel A has an amount of 2y, and vessel B has an amount of 5y + 2y = 7y (from Eq. 2). Thus, the ratio of the amount in vessel A to the amount in vessel B is 2y/7y = 2/7.

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Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and  [#permalink]

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_________________ Re: Two vessels A and B contain milk and water mixed in the ratio 8:5 and   [#permalink] 10 Apr 2019, 05:04
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