Multiple choice

A container contains 125 litres of pure milk. One-fifth of the milk is replaced by water. Again, the same operation is performed and one-fifth of mixture is replaced by water. Find the final ratio of milk to water in the container.

  1. 16 : 9

  2. 17 : 8

  3. 18 : 11

  4. 21 : 9

  5. 21 : 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After two replacements of 1/5 of the mixture, the remaining milk is 125 * (4/5) * (4/5) = 80 litres. The water content is 125 - 80 = 45 litres. The ratio of milk to water is 80:45, which simplifies to 16:9.

AI explanation

Applying the successive replacement formula, the final quantity of milk remaining is Initial Milk times (1 - Replaced Fraction)^n. With an initial quantity of 125 litres and replacing one-fifth of the mixture twice, the milk left is 125 times (4/5)^2, which equals 125 times 16/25, giving 80 litres of milk. The total capacity remains 125 litres, so the volume of water is 125 - 80 = 45 litres. The final ratio of milk to water is 80:45, which simplifies to 16:9.

Keep practicing — related questions