Multiple choice

A 75% milk-and-water solution (say X) is diluted to a 60% milk-and-water solution by adding water to it. Then, 20 L of the solution is replaced and replenished by only 16 L of water so that the final solution (say Y) has 50% milk in it. Find the volume, in L, of solution X.

  1. 60

  2. 120

  3. 40

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The problem describes a series of dilutions and replacements. Given the complexity and potential for missing variables, the provided answer 'None of the above' is a safe choice if the calculation does not match the options.

AI explanation

Using the formula for replacement, replacing 20 L from a 60% solution to get a 50% solution means 0.60 * (V - 20) = 0.50 * (V - 4), which simplifies to 0.10 * V = 10, giving an initial volume V of 100 L. However, diluting a 75% solution to 60% by adding water means the ratio of initial to final volume is 4 to 5, so the initial volume X must be 80 L, not 100 L. The mathematical contradictions in the premises mean no single volume can satisfy the conditions.

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