Multiple choice

A Barrel is completely filled with acetone. 20% of the acetone is replaced by water. This is done 2 more times. What is the final % of acetone remaining in the barrel ?

  1. <font face="MathJax_Main">51.2%</font>

  2. 50%

  3. 66%

  4. 70%
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A Correct answer
Explanation

Initial acetone = 100%. After 3 replacements of 20%: 100 * (1 - 0.2)^3 = 100 * (0.8)^3 = 100 * 0.512 = 51.2%.

AI explanation

Use the standard replacement formula for mixtures, which is Final Amount equals Initial Amount multiplied by (1 minus Replacement Fraction) raised to the power of the number of times the replacement is performed. Here, 20 percent is replaced each time, so the remaining fraction is 0.8, and this action is performed a total of 3 times. Calculate the final percentage of acetone as 100 multiplied by 0.8 cubed, which yields 51.2 percent.

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