Multiple choice

The ratio of milk and water in a container is 2 : 3. When 60 liters of mixture is taken out and replaced with water then the ratio of milk and water becomes 1 : 2. Then find the total capacity of the container.

  1. 360 liters

  2. 220 liters

  3. 440 liters

  4. 350 liters
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A Correct answer
Explanation

Let initial milk be 2x and water 3x. Removing 60L removes 24L milk and 36L water. After adding 60L water, milk is 2x-24 and water is 3x-36+60 = 3x+24. Ratio (2x-24)/(3x+24) = 1/2. Solving gives x=72. Total capacity = 5x = 360.

AI explanation

Let the total capacity of the container be V liters; the initial amounts of milk and water are 2V/5 and 3V/5 respectively. When 60 liters of the mixture is removed, 2/5 of it is milk, meaning 24 liters of milk and 36 liters of water are taken out. Replacing this with 60 liters of water leaves (2V/5 - 24) liters of milk and (3V/5 + 24) liters of water. The new ratio of milk to water is 1 : 2, so 2 multiplied by (2V/5 - 24) equals (3V/5 + 24). Solving 4V/5 - 48 = 3V/5 + 24 gives V/5 = 72, resulting in V = 360 liters.

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