Multiple choice

Two casks A and B contain milk and water in the ratio 2 : 1 and 1 : 2, respectively. In what ratio should the mixture in them be mixed so that the resultant mixture contains milk and water in ratio 1 : 1?

  1. 2 : 3

  2. 1 : 1

  3. 4 : 7

  4. 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the amount from A and y be the amount from B. Milk in A = 2/3, Milk in B = 1/3. Target = 1/2. (2/3)x + (1/3)y = (1/2)(x+y). Multiply by 6: 4x + 2y = 3x + 3y, so x = y. Ratio is 1:1.

AI explanation

Using the rule of alligation, the proportion of milk in cask A is 2/3 and in cask B is 1/3, while the desired proportion in the final mixture is 1/2. The ratio of the quantity taken from cask A to the quantity taken from cask B is proportional to the differences between their individual milk proportions and the target proportion. This gives the ratio as (1/2 - 1/3) : (2/3 - 1/2), which simplifies to 1/6 : 1/6, resulting in a required mixing ratio of 1:1.

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