Multiple choice

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?

  1. 2:5

  2. 4:7

  3. 7:1

  4. 9:1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 12L milk, 8L water. Remove 10L (ratio 3:2 means 6L milk, 4L water removed). Remaining: 6L milk, 4L water. Add 10L milk: 16L milk, 4L water. Repeat: Remove 10L (ratio 4:1 means 8L milk, 2L water removed). Remaining: 8L milk, 2L water. Add 10L milk: 18L milk, 2L water. Ratio = 18:2 = 9:1.

AI explanation

Use the replacement formula, where the final quantity of water equals the initial amount multiplied by (1 - replaced volume / total volume) raised to the number of replacements. The initial water is 2/5 of 20 liters, which is 8 liters. After replacing 10 liters twice, the water left is 8 multiplied by (1/2) squared, resulting in 2 liters, leaving 18 liters of milk in the 20-liter vessel. Therefore, the final ratio of milk to water is 18:2, which simplifies to 9:1.

Keep practicing — related questions