Multiple choice

A mixture contains Milk and Water in the ratio 3 : 2 and another mixture contains them in the ratio 4 : 5. How many litres of the latter must be mixed with 3 L of the former so that the resulting mixture may contain equal quantities of the Milk and Water?

  1. 5.66 L

  2. 4.5 L

  3. 5.4 L

  4. 6 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mixture 1: 3L has 1.8L milk, 1.2L water. Mixture 2: ratio 4:5, let x be volume, milk = 4x/9, water = 5x/9. Total milk = 1.8 + 4x/9, total water = 1.2 + 5x/9. Equating: 1.8 + 4x/9 = 1.2 + 5x/9. 0.6 = x/9, x = 5.4 L.

AI explanation

Using the mixture equation method, let the required volume of the second mixture be y liters. The first mixture has a milk fraction of 3/5, the second has a milk fraction of 4/9, and the final desired milk fraction is 1/2. Setting up the equation for 3 liters of the first mixture plus y liters of the second mixture gives (3 times 3/5) plus (y times 4/9) equals (3 plus y) times 1/2. Solving this yields 9/5 plus 4y/9 equals 3/2 plus y/2, which results in y/18 equals 3/10 and y equals 5.4 L.

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