Multiple choice

A bucket is filled with syrup. Half of its content is poured out and replaced with water. If this process of pouring out half of the content and replacing it with water is repeated five more times, then the final ratio of syrup to water in the bucket is

  1. 1 : 31

  2. 1 : 63

  3. 1 : 32

  4. 1 : 64

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial syrup = 1. After 6 operations of replacing half: Syrup remaining = 1 * (1/2)^6 = 1/64. Water = 1 - 1/64 = 63/64. Ratio = 1/64 : 63/64 = 1 : 63.

AI explanation

Using the replacement formula, the final amount of syrup is the initial amount multiplied by (1 minus the fraction taken out) raised to the number of times the process is done. Since half the contents are replaced six times in total, the remaining syrup fraction is (1/2)^6, which is 1/64 of the original mixture. The remaining 63/64 of the mixture is water, making the final ratio of syrup to water 1 to 63.

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