Milk and Water

Problem

Two beakers have an equal amount of water and milk, one containing all water, the other all milk. A teaspoonful of milk is transferred to the water from the first beaker and then stirred. Then a teaspoonful of the mixture is transferred back to the first beaker. Is there now more water in the milk or more milk in the water? What happens if the mixture is not stirred?

Solution


Let each beaker contain x cc's (cm3)
let a teaspoon contain y cc's.

After first operation 1 teaspoon of milk has been removed from milk beaker and placed in water.
There are (x-y) cc's of milk left in A, x cc's of water and y cc's milk in B
The water and milk in B are in present in the ratio x/y Assuring the mixture is well mixed then one cc of liquid in B will contain x/(x+y) cc's of water and y/(x+y) cc's milk. Teaspoon back which contains y cc's liquid will have xy/(x+y) cc's water and (y*y)/(x+y) cc's milk. Thus the mount of milk in A an end will be at end (x-y)+y2/(x+y)= x2/(x+y) and the amount of water in A will be xy/(x+y).
Thus the ratio of water to milk in A at will be y/x
The amount of milk left in B will be y-y2/(x+y)=xy(x+y)
The amount pf water left in B will be x-xy/(x+y)=x2/(x+y)
Thus the ratio of milk to water in B will be y/x

Same amount of milk in the water in beaker B as water in the milk in A.