Multiple choice

Three containers – A, B and C contain equal volumes of milk-and-water solution with the respective concentrations of milk in them being 60%, 70% and 𝑎%. When the contents in the three containers are completely mixed, the ratio of milk to water in it becomes 11 : 7. How many litres of the solution in container C should be mixed with 10 L of an 80% milk-and-water solution to obtain a 60% milk-and-water solution?

  1. 22.5

  2. 30

  3. 28

  4. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the volume of each container be V. Total milk = 0.6V + 0.7V + (a/100)V. Total volume = 3V. Ratio 11:7 means milk fraction is 11/18. So (1.3 + a/100)V / 3V = 11/18. 1.3 + a/100 = 11/6 = 1.833. a/100 = 0.533, so a = 53.33%. For the second part, using the mixture rule: (10 * 0.8 + V * 0.533) / (10 + V) = 0.6. 8 + 0.533V = 6 + 0.6V. 2 = 0.066V. V = 30.

AI explanation

Let the equal volume in each container be V, so the total volume of the mixture is 3V. The milk is 0.60V, 0.70V and 0.0aV, and the given ratio of milk to water (11:7) means milk is 11/18 of the total. Thus, (1.30V + 0.0aV) divided by 3V equals 11/18, giving a = 50. Now, use the method of alligation to mix an 80% milk solution with a 50% milk solution to get a 60% milk solution. The ratio of their quantities is (60 - 50) to (80 - 60), which is 10:20 or 1:2. For 10 litres of the 80% solution, you need 10 times 2, which is 30 litres of the 50% solution.

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