# A Milky Problem – Milk and Water Solution Puzzle

**An Intriguing Mixture and Alligation Puzzle**

We have two one litre bottles. One contains quart of milk and the other quart of water. (1 quart = 0.9463 liters) We take a tablespoonful of milk and pour it into the water. Then we take a tablespoon of this new mixture (water and milk) and pour it into the bottle of milk. Is there more milk in the water bottle, or more water in the milk bottle?

To solve the problem, we can figure this out in any of the usual ways— often referred to as “mixture and alligation problems”—or we can use some clever logical reasoning to find out the problem’s solution.

Post your solutions below as comment.

4 Comments

Q: Is there more milk in the water bottle, or more water in the milk bottle?

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There will be more milk(percentage wise) in water bottle as compared to water(percentage wise) in the milk bottle, because we took a tablespoonful of milk and poured it into the water. Then we took a tablespoon of this new mixture (water and milk) and pour it into the bottle of milk.

=> proportion of water(out of milk & water mixture) taken from water bottle is lesser as compared to milk in water bottle (as it was 100% milk which was taken from milk bottle , but secondly the mixture of water & milk was taken from water bottle).

**If we go by “total” quantity wise then : total Quantity of milk & water mixture in MILK bottle = total Quantity of milk & water mixture in WATER bottle.

volume of milk in water bottle is comparately more. we are pouring 1 tablespoon of milk in 1 quart of water. from the mixture of milk and water in water bottle, when we take out 1tablespoon of it and add it to milk bottle, now the proportion of water in milk bottle is obviously less than 1 tablespoon. but proportionately milk in water bottle was 1 tablespoon. when 1 tablespoon of mixture is taken out, proportion of milk in the spoon is quite negligible. so maximum milk remains in water bottle.

More milk in the water bottle compared to vol of water in the Milk bottle.

Because, when we pour milk into the water bottle, we are pouring 1 tablespoon (say 10ml) but when we are pouring the mixture into the milk bottle, we are pouring a mixture containing milk and water (10ml of mixture containing some milk with water).

there will be more milk contained in the water bottle..