Multiple choice

A vessel contains 79.99 litres of a mixture of milk and water in which 20.13% of water. If 24.99% of the mixture is taken out and x litres of water is added to the mixture, then the ratio of milk to water becomes 12:5. Find the value of x.

  1. 7

  2. 8

  3. 6

  4. 21

  5. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture is 79.99 L. Removing 24.99% leaves 75% of the original volume, which is approximately 60 L. With 20.13% water, the milk is 47.93 L and water is 12.07 L. After adding x litres of water, the ratio of milk to water becomes 12:5, leading to the equation 47.93 / (12.07 + x) = 12/5, which solves for x approximately equal to 8.

AI explanation

Approximating the given values, the vessel contains 80 liters of mixture with 20% water, meaning there are 16 liters of water and 64 liters of milk. Removing 25% of the mixture takes away 4 liters of water and 16 liters of milk, leaving 12 liters of water and 48 liters of milk. Adding x liters of water gives a ratio of 48 to (12 plus x), which is set equal to 12 to 5, resulting in 240 = 144 plus 12x; therefore, x equals 8.

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