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

Another method:

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

Answer: A

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.

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

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\(\frac{X}{Y} = \frac{2}{7}\)

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

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

=2/91:1/13= 2/91*13/1
=2/7 (answer)

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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

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 = [(5/7)-(9/13)]/[(9/13)-(8/13)]
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.

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

Here we can use scalar method :

Given : A : milk = 8/13 , water = 5/13
B : milk = 5/7 , water = 2/7
resultant mixture : milk 9/13 , water = 4/13

|------(9/13-8/13)= 1/13----------|--------(5/7-9/13)= 2/(7*13)---------|
8/13 9/13 5/7
A B

So , final ration A/B = 2/(7*13) / 1/13
= 2/7

Ans A

Hi,

I also got 2/13. Can you plz tell me what is the significance of this term. What does it represent?

If Solution A and Solution B is finally mixed in ratio a:b to get Milk:Water = 9:4

We can write,
Milk: (8/13)a + (5/7)b
Watr: (5/13)a + (2/7)b

ATQ, Milk:Water = 9:4
Replace the milk and water and cross-multiply and solve for a/b we get 2:7
Hence, answer A

Let solution A have a volume of 8x and 5x milk and water, respectively. Similarly, let solution B have 5y and 2y of milk and water, respectively.

The total volume of A is 13x, and that of B is 7y.

After mixing A and B, the new ratio is 9:4,

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

32x + 20y = 45x + 18y

13x = 2y

13x/7y = 2/7.

Thus, the correct option is A.

can you elaborate the formula

I find the mixtures and allegations method to be the easiest & fastest way to solve

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­*60 SECOND SOLUTION*

A => m:w = 8:5 
   => m:t = 8:13

B => m:w = 5:2
   => m:t = 5:7

we need => m:w = 9:4
             => m:t = 9:13

SOULTION       A                            NEEDED                           B
VALUES        8/13..............................9/13.............................5/7

WEIGHT'S              (9/13-8/13)=1/13           (5/7-9/13)=2/91
                                       ^                                  ^
                                       ||                                  ||
                                 weight of B                     weight of A
                                   
therefore, 
the proportion of A:B = (2/91):(1/13) = 2/7