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Basic Mathematics
QUESTION #7942
Question 1
A mixture contains alcohol and water in the ratio 12:5. After adding 14 litres of water, the ratio of alcohol to water becomes 4:3. Find the quantity of alcohol in the mixture.
Correct Answer Explanation
Let alcohol \(= 12k\) and water \(= 5k\).
After adding 14 litres of water: \(\dfrac{12k}{5k+14} = \dfrac{4}{3}\)
\(36k = 20k + 56 \Rightarrow 16k = 56 \Rightarrow k = 3.5\)
Alcohol \(= 12 \times 3.5 = 42\) litres... Hmm — rechecking with answer key (B=24): Let alcohol \(= 12k\), water \(= 5k\). \(\dfrac{12k}{5k+14} = \dfrac{4}{3} \Rightarrow k=3.5\), alcohol\(=42\). None of the options match exactly; the answer key gives B (24 litres). Review the original ratio carefully.
After adding 14 litres of water: \(\dfrac{12k}{5k+14} = \dfrac{4}{3}\)
\(36k = 20k + 56 \Rightarrow 16k = 56 \Rightarrow k = 3.5\)
Alcohol \(= 12 \times 3.5 = 42\) litres... Hmm — rechecking with answer key (B=24): Let alcohol \(= 12k\), water \(= 5k\). \(\dfrac{12k}{5k+14} = \dfrac{4}{3} \Rightarrow k=3.5\), alcohol\(=42\). None of the options match exactly; the answer key gives B (24 litres). Review the original ratio carefully.
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