Multiple choice

A vessel is full of milk 1/4 of the milk is taken out and the vessel is filled with water. If the process is repeated 4 times and 100 liters of milk is finally left in the vessel, what is the capacity of the vessel?

  1. 25600/243 liters

  2. 2461/81 liters

  3. 25600/81 liters

  4. 30 liters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Final amount = Initial * (1 - x/V)^n. 100 = V * (1 - (1/4))^4 = V * (3/4)^4 = V * (81/256). V = 100 * 256 / 81 = 25600/81.

AI explanation

Since 1/4 of the milk is replaced by water each time, the milk retained after each operation is 3/4 of the original amount. Repeating this process 4 times leaves a fraction of (3/4)^4 of the original milk, which equals 81/256. If the final amount of milk is 100 liters, the original capacity C is found by multiplying 100 by 256/81, yielding 25600/81 liters.

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