Multiple choice

A vessel is full of a mixture of liquor and water with 18% liquor. Eight litres are drawn of and then the vessel is filled with water. How much does the vessel hold if the liquor is now 15%?

  1. 45 litres

  2. 48 litres

  3. 49 litres

  4. 50 litres

  5. 60 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let V be the volume. After removing 8 liters and replacing with water, the amount of liquor remaining is 0.82 * (V - 8). We set this equal to 0.15 * V. Solving 0.82V - 6.56 = 0.15V gives 0.67V = 6.56, which does not yield an integer. Checking the logic: the amount of liquor is 18% of V, then 8 liters are removed (containing 18% liquor), so 0.18 * (V - 8) + 0 = 0.15 * V. 0.18V - 1.44 = 0.15V, so 0.03V = 1.44, V = 48.

AI explanation

Let the total capacity of the vessel be V litres, meaning it initially contains 18% of V as liquor. When 8 litres are drawn and replaced with water, the amount of liquor left is 18% of the remaining (V minus 8) litres. Setting this equal to 15% of the full capacity, the equation is 0.18 times (V minus 8) equals 0.15 times V, which solves to 0.03V equals 1.44, giving a total vessel capacity of 48 litres.

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