Multiple choice

Six litres are drawn from a cask full of wine. It is filled with water. Six litres of mixture are again drawn and the cask is again filled with water. The ratio of quantity of wine left in the cask to that of water is 25 : 24. How much of mixture can the cask hold?

  1. 26 litres

  2. 21 litres

  3. 25 litres

  4. 32 litres

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the capacity be V. After two replacements of 6 litres, the wine remaining is V * (1 - 6/V)^2. The ratio of wine to water is 25:24, so wine is 25/49 of the total volume. V * (1 - 6/V)^2 = (25/49) * V. (1 - 6/V)^2 = 25/49. 1 - 6/V = 5/7. 6/V = 2/7. V = 21.

AI explanation

Let the total capacity of the cask be V litres. Using the formula for repeated replacement, the ratio of wine left to the initial amount is (1 - 6/V)^2. The given ratio of wine to water is 25 to 24, meaning the ratio of remaining wine to the total capacity is 25 to (25 + 24), or 25 to 49. Setting up the equation (1 - 6/V)^2 = 25/49 and taking the square root of both sides gives 1 - 6/V = 5/7, which results in V = 21 litres.

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