Two vessels A and B contain milk and water mixed in the ratio 8:5 and

Question

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

chetan2u · Accepted Answer

Hi,
 your OA is wrong ..
 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

chetan2u · Answer

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}

Kurtosis · Answer

Another method:

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

Answer: A

ranaazad · Answer

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

Could someone please clarify?
Regards.

Could someone please clarify? Regards.

gracie · Answer

8A/13+5B/7=9/13(A+B)
A/B=2/7
A:B=2:7

sasyaharry · Answer

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}

gps5441 · Answer

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)= ÷ =2/91÷1/13=2/7 or 2:7 answer is =A

JeffTargetTestPrep · Answer

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.

Answer: A

coylahood · Answer

Using equations can be very time-consuming and tedious. The best approach is to use the alligation technique. In order to determine the ratio in which the contents of Vessel A need to be mixed with those of Vessel B to arrive at a ratio of milk to honey of 9:4, we need to work entirely with either the ratios for milk or those of water. Working entirely with the ratios for milk, we know that the ratio of milk to water in Vessel A is 8:5. Therefore, the fraction of milk in vessel A is 8/13. Likewise, the ratio of milk to water in vessel B is 5:2. Therefore, the fraction of milk in the vessel is 5/7. Finally, because the ratio of milk to water in the mixture is 9:4, the fraction of milk in the mixture is 9/13.
These three quantities can be used to estimate the ratio of A:B as follows
A:B =  / 
To simplify the calculations, let's multiply all through by the LCM of 7 and 13 which is equal to 91.

Therefore
A:B = (65-63)/(63-56) = 2/7.
Therefore, the ratio of A:B that leads to a mixture with milk in the ratio 9:4 is 2:7.
So the correct answer is choice A.

coylahood · Answer

hsingh3031 · Answer

We can take both the solutions A & B as 91A & 91B as 91 is 13X7 . So,

56 A + 65 B = 63 A + 63B

2B = 7A
 
Hence A/B = 2 / 7. Option A

ria99 · Answer

why cant we do this using LCM of denominators? I am confused with the approach used in mixture problems involving fractions and ratios. My assumption was that its always easier to assume a number in such cases

egmat · Answer

Hi ria99,

Good news: you absolutely  can  use the LCM of the denominators here. In fact, two posters in this thread already did exactly that (hsingh3031 used 91A and 91B; coylahood multiplied the alligation through by  91 ). So your instinct isn't wrong - let me show where it fits in.

First set up the milk equation, the same one gracie and sasyaharry wrote:

- Milk from A =  8/13 · a 
- Milk from B =  5/7 · b 
- Total milk wanted =  9/13 · (a+b)

So:  8a/13 + 5b/7 = 9(a+b)/13 .

Now bring in your LCM idea. The LCM of  13  and  7  is  91 . Multiply every term by  91  to clear all fractions:

- 8a/13 · 91 =  56a 
- 5b/7 · 91 =  65b 
- 9(a+b)/13 · 91 =  63(a+b)

That gives 56a + 65b = 63a + 63b →  2b = 7a  →  a/b = 2/7 . Answer  A . So LCM didn't fail you - it's just the clearing-denominators step, used  after  you write the equation.

Why "just assume a number" feels stuck here

Assuming a convenient number is great when the unknown is some property  inside  one fixed mixture. But here the thing being asked  is the ratio in which you combine A and B  - that ratio (a : b) is the unknown itself. You can't assume it; you have to solve for it. So you keep a and b as unknowns, write the milk balance, and let the algebra (cleared by the LCM  91 ) hand you a : b.

Quick way to feel the difference:

-  "Vessel A is 8:5 milk:water - what fraction is milk?"  → here you can assume  13 liters  and read off  8/13  instantly.
-  "In what ratio do I mix A and B to hit 9:4?"  → the ratio is the answer, so assuming it would beg the question.

Bottom line: set up the equation, then use your LCM trick to clear fractions - both methods you mentioned are valid, just used at the right moment.

Answer: A

Two vessels A and B contain milk and water mixed in the ratio 8:5 and

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Two vessels A and B contain milk and water mixed in the ratio 8:5 and

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