Multiple choice

A chemist has three types of liquids: Liquid X, Liquid Y, and Liquid Z. The ratio of X to Y in the first mixture is 2 : 5, and the ratio of Y to Z in the second mixture is 3 : 4. The chemist wants to create a final mixture by combining the first and second mixtures such that the ratio of X to Z is 1 : 2. If the chemist needs 60 litres of the final mixture, how many litres of each mixture should be used?

  1. 30 litres of the first mixture, 30 litres of the second mixture

  2. 15 litres of the first mixture, 45 litres of the second mixture

  3. 12 litres of the first mixture, 48 litres of the second mixture

  4. 20 litres of the first mixture, 40 litres of the second mixture

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

Let M1 be the first mixture and M2 be the second. M1 has X:Y = 2:5. M2 has Y:Z = 3:4. To combine, we need a common Y. M1: X:Y = 6:15. M2: Y:Z = 15:20. Thus, M1 has X:Y:Z = 6:15:0 and M2 has X:Y:Z = 0:15:20. Let a be volume of M1 and b be volume of M2. Total X = (6/21)a. Total Z = (20/35)b = (4/7)b. We want X/Z = 1/2. (6/21)a / (4/7)b = 1/2 => (2/7)a / (4/7)b = 1/2 => a/2b = 1/2 => a = b. Since a+b = 60, a=30 and b=30.

AI explanation

Assume the first mixture has 0 amounts of Z and the second has 0 amounts of X to simplify. Using weighted averages, combining the mixtures means we take the ratio of X from the first and Z from the second. Testing the given options to see which satisfies a 1:2 ratio of X to Z reveals that 30 litres of the first mixture and 30 litres of the second mixture is the required combination.

Keep practicing — related questions