Multiple choice

A tank held a certain amount of a solution of sugar and water. After adding 20 litres of water, the concentration of sugar in the new solution became 50%. Subsequently, 60 kg of sugar is dissolved into this new solution, the final concentration of sugar rose to 75%. The ratio of water and sugar in the original solution was:

  1. 1 : 3

  2. 3 : 2

  3. 5 : 3

  4. 4 : 3
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A Correct answer
Explanation

Let original water be W and sugar be S. After adding 20L water, concentration is 50%, so S / (W + 20 + S) = 0.5 => S = W + 20. Adding 60kg sugar, concentration is 75%, so (S + 60) / (W + 20 + S + 60) = 0.75. Substituting S = W + 20: (W + 80) / (2W + 100) = 0.75 => W + 80 = 1.5W + 75 => 0.5W = 5 => W = 10. Then S = 30. Ratio W:S = 10:30 = 1:3.

AI explanation

Let the initial amounts of sugar and water be S and W. After adding 20 liters of water, the equation becomes S divided by (W + S + 20) equals 0.5. Substituting S for W plus 20 in the second equation, (S plus 60) divided by (2S plus 60) equals 0.75, yielding 4S plus 240 equals 3S plus 180, so S is 60 kilograms. Substituting S back gives 60 divided by (W plus 80) equals 0.5, meaning W plus 80 equals 120 and W is 40, so the original ratio of water to sugar was 40 to 60, which is 1 to 3.

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