Multiple choice

A milkman has a vessel containing 40 litres of milk. He delivers 10 litres to the first house, and adds an equal quantity of water to the vessel. He does exactly the same at the second and third houses. What is the ratio of milk and water when he has finished delivering at the third house and added 10 litres of water?

  1. 27 : 37

  2. 26 : 38

  3. 1 : 4

  4. 27 : 64
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A Correct answer
Explanation

The amount of milk remaining after 3 operations is 40 * (1 - 10/40)^3 = 40 * (3/4)^3 = 40 * 27/64 = 16.875. The water is 40 - 16.875 = 23.125. The ratio 16.875 : 23.125 simplifies to 27 : 37.

AI explanation

Each time the milkman removes 10 liters from a 40 liter vessel, 75% of the milk remains, meaning he retains three-fourths of the milk after each house. After three such replacements, the remaining milk is 40 multiplied by three-fourths cubed, which equals 40 multiplied by 27 divided by 64, yielding 16.875 liters. Since the total volume remains 40 liters, the water present is 40 minus 16.875, giving 23.125 liters, and the ratio of milk to water is 16875 to 23125, which simplifies to 27 to 37. The option stating 27 to 37 is therefore correct.

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