A 60% milk solution is diluted to 50% by adding water equivalent to one-fifth of its total volume. Then 15L of the solution is replaced by water so that the final solution has 40% milk in it. Which of the following gives the initial volume of the solution?

Using the mixture dilution formula, let the initial volume be V. Replacing 15 L from V L of 50% milk to get 40% milk means 0.50 * (V - 15) = 0.40 * V, which gives 0.10 * V = 7.5, so V = 75 L. However, a 60% solution only becomes a 50% solution if the added water equals one-third of the original volume, not one-fifth, making the premise and the answer mathematically inconsistent. Therefore, no initial volume satisfies these conditions.

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