A butler stole wine from a bottle which contained 32% spirit and then replaced what he stole with wine containing only 18% spirit. The bottle was then 24% strength. How much of the bottle had he stolen?

By using the method of alligation, we calculate the differences in spirit percentages to infer that the butler stole approximately 42.86% of the original wine from the bottle.

Explanation:

This problem can be solved using the method of alligation, a technique often used in Mathematics to handle questions concerning mixtures. Firstly, consider the initial content of the bottle with the spirit strength of 32%. Secondly, take into account the wine that was added, having only 18% spirit strength. With these two facts, we know that the final spirit strength ended up being 24%, which is in the middle of 18% and 32%.

Now, we apply the alligation rule, which requires finding the difference between each of the initial percentages (18 and 32) and the final percentage (24). The difference between 32% and 24% is 8%, and the difference between 18% and 24% is 6%. These differences tell us the ratio in which the original wine and the added wine contribute to the final mixture, so we can infer that the butler stole 6/14 = 42.86% of the original bottle.

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