Multiple choice

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

  1. 4 : 9

  2. 1 : 3

  3. 5 : 9

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

Let initial coffee be 1. After two removals of fraction 'x', coffee remaining = (1-x)^2. Given (1-x)^2 = 16/25 (since coffee:cocoa is 16:9, total is 25). So 1-x = 4/5, x = 1/5. In mixture P, coffee = 4/5, cocoa = 1/5. In mixture Q, coffee = 16/25, cocoa = 9/25. Ratio of cocoa in P to Q = (1/5) / (9/25) = 5/9.

AI explanation

Using the repeated replacement formula, the final ratio of coffee to the total mixture in Q is 16 / 25. The fraction of liquid replaced each time is the square root of 16 / 25, which is 4 / 5. Thus, mixture P has a coffee to total ratio of 4 / 5, meaning its cocoa to total ratio is 1 / 5. Therefore, the ratio of cocoa in mixture P to that in mixture Q is (1 / 5) : (9 / 25), which simplifies to 5 : 9.

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