Multiple choice

A chemist has two alcohol solutions, one containing 40% alcohol and the other containing 60% alcohol. How much of each should be mixed to get 100 litres of a 50% alcohol solution?

  1. 60 litres of solution having 40% alcohol and 40 litres of solution having 60% alcohol

  2. 50 litres of each solution

  3. 40 litres solution having 40% alcohol and 60 litres of solution having 60% alcohol

  4. 70 litres of solution having 40% alcohol and 30 litres of solution having 60% alcohol

  5. 30 litres of solution having 40% alcohol and 70 litres of solution having 60% alcohol
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the allegation rule or a system of equations: 0.4x + 0.6(100-x) = 0.5(100). 0.4x + 60 - 0.6x = 50. -0.2x = -10. x = 50. Thus, 50 liters of each solution are needed.

AI explanation

Using the rule of alligation, the ratio of the first solution to the second solution is (60 - 50) : (50 - 40), which equals 10 : 10 or 1 : 1. The total mixture required is 100 litres, so dividing it in a 1 : 1 ratio gives 50 litres of each. Therefore, the chemist should mix 50 litres of the 40 percent solution and 50 litres of the 60 percent solution.

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