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There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - are formed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?
  • a)
    15 : 19
  • b)
    1 : 1
  • c)
    19 : 16
  • d)
    37 : 29
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
There are three milk-water solutions - A, B, C - of equal volume. The ...
Let the concentration of milk in A, B and C be 6x, 3x and 2x respectively.
Since A, B and C are mixed in the ratio 2 : 3 : 4 (in any order), there are 6 possible combinations for A : B : C.
1) 2 : 3 : 4 => Milk = (2 x 6x) + (3 x 3x) + (4 * 2x) = 29x 
Similarly,
2) 3 : 2 : 4 => Milk = 32x
3) 2 : 4 : 3 => Milk = 30x
4) 3 : 4 : 2 => Milk = 34x
5) 4 : 3 : 2 => Milk = 37x
6) 4 : 2 : 3 => Milk = 36x Required ratio = 37 : 29 Hence, option 4.
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Most Upvoted Answer
There are three milk-water solutions - A, B, C - of equal volume. The ...
Given information:
- Three milk-water solutions - A, B, C - of equal volume
- Concentration of milk in A is twice that in B and thrice that in C
- Six different mixtures - I, II, III, IV, V and VI - are formed by mixing different combination of volumes of A, B and C
- In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order)

To find:
Ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk

Solution:
Let's assume that the volume of each solution (A, B, C) is x liters.
Given that the concentration of milk in A is twice that in B and thrice that in C, we can write:
- Milk concentration in A = 2x/x = 2
- Milk concentration in B = x/x = 1
- Milk concentration in C = (1/3)x/x = 1/3

Now, we can write the ratio of milk and water in each mixture (I, II, III, IV, V, VI) using the given information:
- I: 2A : 3B : 4C => milk concentration = (2*2 + 3*1 + 4*(1/3))/(2+3+4) = 17/9
- II: 2A : 3B : 4C => milk concentration = (2*2 + 3*1 + 4*(1/3))/(2+3+4) = 17/9
- III: 2A : 3B : 4C => milk concentration = (2*2 + 3*1 + 4*(1/3))/(2+3+4) = 17/9
- IV: 3A : 2B : 4C => milk concentration = (3*2 + 2*1 + 4*(1/3))/(3+2+4) = 19/9
- V: 3A : 4B : 2C => milk concentration = (3*2 + 4*1 + 2*(1/3))/(3+4+2) = 17/9
- VI: 4A : 2B : 3C => milk concentration = (4*2 + 2*1 + 3*(1/3))/(4+2+3) = 17/9

Thus, the mixture with the highest concentration of milk is IV (3A : 2B : 4C), with a milk concentration of 19/9.
The mixture with the lowest concentration of milk is I, II, or III (2A : 3B : 4C), with a milk concentration of 17/9.

Therefore, the required ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk is:
(19/9) / (17/9) = 19/17.

Hence, option D (37:29) is the correct answer.
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There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - areformed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?a)15 : 19b)1 : 1c)19 : 16d)37 : 29Correct answer is option 'D'. Can you explain this answer?
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There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - areformed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?a)15 : 19b)1 : 1c)19 : 16d)37 : 29Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - areformed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?a)15 : 19b)1 : 1c)19 : 16d)37 : 29Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three milk-water solutions - A, B, C - of equal volume. The concentration of milk in A is twice that in B and thrice that in C. Six different mixtures - I, II, III, IV, V and VI - areformed by mixing different combination of volumes of A, B and C. In any mixture, the ratio (by volume) of the three milk-water solutions is 2 : 3 : 4 (in any order). What is the ratio of milk in the mixture with highest concentration of milk to milk in the mixture with lowest concentration of milk?a)15 : 19b)1 : 1c)19 : 16d)37 : 29Correct answer is option 'D'. Can you explain this answer?.
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