What's wrong with my math solution?

Question

I have ten liters of milk. I take out one liter and replace it with one liter of water. I do the process a second time. How much milk do I have in final product.
 I figured I have 9/10 after first process and then 8/10 of milk after second. but the answer is 81% milk

Answer

You have to find 10% of 100 which is 10.   100 - 10 = 90 Then find 10% of 90 which is 9.   90 - 9 = 81. Therefore the % of milk is 81%.

Answer

One liter out of ten equals 1/10-th of the total. After replacing the milk with the water you thoroughly stir the liquid. Now, in every sample of the liquid you've got 1/10 of water and 9/10 of milk. Repeating the replacement involves taking one liter of that already diluted milk, thereby removing 900ml = 9/10 liter of milk. In total you've taken 1.9 l of milk out of 10 l. That's 19%.  10 - 1.9 = 8.1  which amounts to 81%.

Answer

After 1st cycle, there is 90%X of milk
After 2nd cycle, there is just 90%(90%X)of milk or 81% or 81/100 of milk

What's wrong with my math solution?

Answers (3)