Multiple choice

A container contains 'X' litres of milk. A thief stole 50 litres of milk and replaced it with the same quantity of water. He repeated the same process further two times. And thus milk in the container is only 'X - 122' litres. Then what is the quantity of milk in the final mixture?

  1. 122 litres

  2. 124 litres

  3. 128 litres

  4. 250 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The formula for the remaining amount of the original substance is X * (1 - r/X)^n. Here, 50 * (1 - 50/X)^3 = 122 is not the correct setup; rather, the amount of milk left is X * (1 - 50/X)^3 = X - 122. Solving for X gives 250. The final quantity of milk is 250 - 122 = 128.

AI explanation

Applying the replacement formula, Final Milk = X multiplied by ((X minus 50) divided by X) raised to the power of 3. The problem states the final milk equals X minus 122, so X multiplied by ((X minus 50) divided by X)^3 equals X minus 122. Solving this equation for X gives an initial volume of 250 litres; substituting this back yields a final milk quantity of 128 litres.

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