Multiple choice

Ishwar had a conical flask which was full of acid. Six litres of acid was removed and replaced by water. Again, 6 litres of the mixture was removed and replaced by water. The proportion of acid left in the flask then was 64/81 of the total mixture (in the flask). What is the capacity of the flask?

  1. 42 litres

  2. 48 litres

  3. 56 litres

  4. 54 litres

  5. 66 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let capacity be V. After two replacements, acid remaining = V * (1 - 6/V)^2. Given (1 - 6/V)^2 = 64/81. Taking square root, 1 - 6/V = 8/9. 6/V = 1/9. V = 54.

AI explanation

Use the replacement formula for mixtures: Final Quantity = Initial Quantity multiplied by ((Capacity minus Replacement) divided by Capacity) raised to the number of operations. Let the capacity be C, giving the equation C times ((C minus 6) divided by C) squared = C times (64/81). This simplifies to ((C minus 6) divided by C) squared = (8/9) squared, so (C minus 6) divided by C equals 8/9. Solving 9C minus 54 = 8C results in a capacity of 54 litres.

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