Multiple choice

8 litres are drawn from a flask containing milk and then filled with water. The operation is performed 3 more times. The ratio of the quantity of milk left and total solution is 81/625. How much milk the flask initially holds?

  1. 10 ltr

  2. 20 ltr

  3. 30 ltr

  4. 40 ltr

  5. None of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a dilution problem. When 8 litres are drawn and replaced with water 4 times, the remaining milk is initial × (1 - 8/V)⁴, where V is initial volume. Given milk remaining/total = 81/625 after 4 operations. Since each operation removes the same fraction, (1 - 8/V)⁴ = 81/625. Taking fourth root: 1 - 8/V = 3/5 (since 3⁴ = 81 and 5⁴ = 625). So 8/V = 2/5, giving V = 20 litres.