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The ratio of liquids $P$ and $Q$ is $5:3$. If 16 L of the mixture is removed and replaced with 16 L of $Q$, the new ratio becomes $4:5$. Find the initial quantity of the mixture.

1. 60 L
2. 70 L
3. 80 L
4. 90 L

Correct answer: 80 L

Solution

If the initial quantity is $V$, then initially $P=\frac{5}{8}V$ and $Q=\frac{3}{8}V$. After removing 16 L, the removed amounts are in the same ratio, and replacing with 16 L of $Q$ changes only the $Q$ part. Using the final ratio $4:5$ gives $V=80$ L.

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