Multiple choice

A chemist has two solutions, one containing 30% alcohol and the other containing 60% alcohol. He wants to create a new solution containing 45% alcohol by mixing these two solutions. However, he accidentally spills 50 ml from the first solution and 30 ml from the second solution on the laboratory floor. Undeterred, he mixes the remaining solutions to get the desired solution. How many millilitres of the first solution and the second solution did the chemist have initially?

  1. 50 ml of the first solution and 40 ml of the second solution

  2. 40 ml of the first solution and 60 ml of the second solution

  3. 45 ml of the first solution and 55 ml of the second solution

  4. 55 ml of the first solution and 35 ml of the second solution

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x and y be the initial volumes. The amount of alcohol is 0.3x + 0.6y. After spilling, the remaining volumes are (x-50) and (y-30), and the mixture is 0.3(x-50) + 0.6(y-30) = 0.45(x-50 + y-30). Solving this linear equation with the constraints provided in the options confirms that 55 and 35 satisfy the conditions.

AI explanation

Using the rule of alligation for the target 45% concentration, the initial ratio of the first solution to the second solution must be 1:1. Because the final mixed amounts are 50 ml and 30 ml, which is a 5:3 ratio, the spilled amounts must have distorted this balance. Subtracting the given spilled amounts from the initial volumes in the correct option yields equal remaining amounts, confirming the initial amounts were 55 ml of the first solution and 35 ml of the second solution.

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