Multiple choice

A bottle is initially filled with sugar syrup. In each step, two fifth of its content is removed and replaced with water. This process is repeated five times. What is the final ratio of syrup to water in the bottle?

  1. 81 : 544

  2. 81 : 625

  3. 243 : 2882

  4. 243 : 3125

  5. a
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C Correct answer
Explanation

If 2/5 is removed, 3/5 of the syrup remains. After 5 steps, the remaining syrup is (3/5)^5 = 243/3125 of the original volume. The water content is 1 - 243/3125 = 2882/3125. The ratio of syrup to water is 243 : 2882.

AI explanation

Using the replacement formula, the final quantity of syrup is calculated as Initial Quantity multiplied by (1 - Replacement Fraction)^n, which gives 1 multiplied by (1 - 2/5)^5. This simplifies to (3/5)^5, resulting in 243/3125 of the bottle being syrup, meaning the rest of the bottle, which is 2882/3125, is water. Therefore, the final ratio of syrup to water is 243 : 2882.

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