Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving

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

Correct Answer: (A)
Solution and Explanation:
Approach Solution 1:

The problem statement frames that

Given:

• Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively

Find out:

• The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

Focus just on one component of the mixture while answering questions like these.

Let us consider the milk component.
How much milk is there in equation A=8/13? (When a ratio is supplied, add the numbers together to get the total.)
The proportion of milk in B = 5/7.
The average milk proportion after combining two solutions or mixes is 9/13.

use the weighted average method
w1/w2=(A2-avg)/(avg-A1). Here, A1 = A and A2 = B.
Avg = 9/13, A1 = 8/13, and A2 = 5/7. (You can use any of the specified values for A1 and A2 and still get the same result.)
w1/w2=(5/7-9/13)(9/13-8/13)=[(65-63)/91][(9-8)/13]=\(2/9 \div11/13\)=2/7 or 2:7.

Approach Solution 2:

The problem statement informs that

Given:

• Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively

Find out:

• The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

The ratios can be made:

A vessel:

Milk: water equals 8: 5, thus 8 + 5 equals 13. (Eq. 1)

B vessel:

Water: milk ratio is 5:2, therefore 5 + 2 = 7. (Eq. 2)

The following equation can be made:
(8x + 5y)/(5x + 2y) = 9/4
4(8x + 5y) = 9(5x + 2y)
32x + 20y = 45x + 18y
2y = 13x (Eq. 3)
Eq. 1 said that 8x + 5x = 13x

We utilise Eq. 3 to claim that vessel A has an amount of 2y and vessel B has an amount of 5y + 2y = 7y (from Eq. 2).
As a result, 2y/7y = 2/7 is the ratio of the amounts in vessels A and B.

Approach Solution 3:

The problem statement states that

Given:

• Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively

Find out:

• The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4

The proportion of milk and water in vessel A is 8:5. Hence, the proportion of milk is 8/13 and water is 5/13
In the same way, the proportion of milk and water in vessel B is 5:2. Hence, the proportion of milk is 5/7 and water is 2/7
The required proportion of milk and water in the new mixture is 9:4. Hence, the proportion of milk is 9/13 and water is 4/13
Let x:y be the ratio in which they are mixed

Hence,
(8/13)*x + (5/7)*y = 9/13
Also, (5/13)*x+ (2/7)*y = 4/13
By solving these two equations, we will get x = 2/9 and y = 7/9

Therefore, x:y = 2:7
Hence the ratio in which they are mixed = 2:7

“Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”. To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. GMAT Quant practice papers cite several sorts of questions that will enable the candidate to polish up their mathematical knowledge.

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