Multiple choice

Maple syrup mixture comes in two concentrations. One contains 15% maple syrup and the other contains 5% maple syrup. How many litres of the second mixture must be added to 20 litres of the first maple syrup solution to make a 10% maple syrup mixture?

  1. 5 l

  2. 10 l

  3. 15 l

  4. 20 l

  5. None of these
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D Correct answer
Explanation

Let x be the amount of 5% solution. (0.15 * 20 + 0.05 * x) / (20 + x) = 0.10. 3 + 0.05x = 2 + 0.10x. 1 = 0.05x, so x = 20.

AI explanation

We can solve this using the method of alligation. The first mixture has a 15% concentration, the second has a 5% concentration, and the desired middle concentration is 10%. The ratio of the quantity of the first mixture to the second mixture is calculated by finding the difference between their concentrations and the target concentration, giving (10 - 5) : (15 - 10). This simplifies to a ratio of 5:5, or 1:1. Since there are 20 litres of the first mixture, an equal amount of 20 litres of the second mixture must be added.

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