Multiple choice

8 litres are drawn from a container full of Milk and is then filled with water. This operation is performed three more times. The ratio of the quantity of Milk now left in the container to that of water is 16 : 65. How much Milk did the container hold originally?

  1. 16 L

  2. 20 L

  3. 24 L

  4. 32 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the original quantity be x. After 4 operations, the remaining milk is x * (1 - 8/x)^4. The ratio of milk to water is 16:65, meaning milk is 16/(16+65) = 16/81 of the total. Thus, (1 - 8/x)^4 = 16/81 = (2/3)^4. Solving 1 - 8/x = 2/3 gives 8/x = 1/3, so x = 24.

AI explanation

Using the formula for repeated replacement, the fraction of pure milk remaining after n operations is ((V minus x) divided by V) raised to the power n, where V is the initial volume and x is the replaced volume. The final ratio of milk to water is 16 to 65, so the fraction of milk remaining is 16 divided by the sum of 16 and 65, which is 16/81. Substituting the known values, the equation becomes ((V minus 8) divided by V) raised to the power 4 equals 16/81, which simplifies to ((V minus 8) divided by V) squared equals 4/9. Taking the square root gives (V minus 8) divided by V equals 2/3, leading to 3V minus 24 equals 2V and V equals 24 L.

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