Multiple choice

The concentration of milk in a 60L milk and water solution is 30%. If 6L of the solution is replaced by water and then 5L of the resulting solution is again replaced by water, then find the concentration of milk in the final solution.

  1. 24.50%

  2. 25.00%

  3. 24.75%

  4. 25.50%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial milk = 0.3 * 60 = 18L. After replacing 6L of solution (10% of total), milk remaining = 18 * 0.9 = 16.2L. After replacing 5L of the new 60L solution (5/60 = 1/12), milk remaining = 16.2 * (1 - 1/12) = 16.2 * (11/12) = 14.85L. Concentration = 14.85 / 60 = 0.2475 = 24.75%.

AI explanation

Using the replacement formula, Final Milk Concentration = Initial Concentration * (1 - Volume Replaced / Total Volume)^n. The initial milk is 30%, and the replacements happen twice, first 6L then 5L. The calculation is 0.30 * (1 - 6/60) * (1 - 5/60) = 0.30 * 0.9 * 0.9166, which equals 0.2475. The concentration of milk in the final solution is 24.75%.

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