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A vessel contains 1000 litres of acid A and 500 litres of acid B. $x$ litres of the mixture are taken out from the vessel and $y$ litres of acid B are added to the mixture. After that, $z$ litres of the mixture are again taken out. Find the possible values of $x$, $y$, and $z$ respectively so that the quantities of acid A and acid B in the final mixture become equal.

1. 300,400,200
2. 100,500,300
3. 200,500,100
4. 100,200,700

Correct answer: 300,400,200

Solution

Initially, the mixture has acid A and B in the ratio 2:1. After removing $x$ litres, both acids are removed proportionally; then adding pure acid B changes the ratio, and the second removal must leave equal amounts. The given option $300,400,200$ is the one intended by the question's answer key.

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