Multiple choice

Harmeet has a bowl, which was full of milk. Four litres of milk was removed and replaced by water. Again, 4 litres of mixture was removed and replaced by water. The proportion of milk left in the bowl was 49/81 of the total mixture (in the bowl). What is the capacity of bowl?

  1. 20 litres

  2. 18 litres

  3. 22 litres

  4. 16 litres

  5. 25 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the capacity be V. After two replacements of 4 litres, the remaining milk is V * (1 - 4/V)^2. Given this is 49/81 V, we have (1 - 4/V)^2 = 49/81. Taking the square root, 1 - 4/V = 7/9. Thus, 4/V = 2/9, so V = 18.

AI explanation

Using the replacement formula where the final proportion of milk equals (1 - y/c)^n, with y as the replaced amount and c as the capacity, we have (1 - 4/c)^2 = 49/81. Taking the square root of both sides gives 1 - 4/c = 7/9, so 4/c = 2/9. Solving this shows that c equals 18, meaning the capacity of the bowl is 18 litres.

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