Multiple choice

A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by the same quantity of liquid B. Again, 4 litres of the mixture is taken out and replaced by the same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

  1. 4 : 1

  2. 5 : 1

  3. 16 : 9

  4. 17 : 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial volume = 20. After two replacements of 4L (which is 1/5 of the total), the amount of A remaining is 20 * (1 - 4/20)^2 = 20 * (0.8)^2 = 20 * 0.64 = 12.8. Amount of B = 20 - 12.8 = 7.2. Ratio A:B = 12.8 : 7.2 = 128 : 72 = 16 : 9.

AI explanation

Using the repeated replacement formula, Final Amount of A equals Initial Amount times the quantity (1 minus Replacement Volume divided by Total Volume) raised to the number of operations. This gives 20 multiplied by (1 - 4/20) squared, resulting in 12.8 litres of liquid A. The total mixture is 20 litres, so liquid B is 7.2 litres, making the final ratio 12.8 to 7.2, which simplifies to 16:9.

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