Multiple choice

Five litres are drawn off from a vessel full of milk and substituted by water. Again five litres of the mixture are withdrawn and is replaced by water. If the vessel now contains milk and water in the ratio 16 : 9, the capacity of the vessel is

  1. 12.5 litres

  2. 25 litres

  3. 20 litres

  4. 15 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let capacity be V. After two operations, milk remaining = V * (1 - 5/V)^2. Ratio of milk to total is 16/25. (1 - 5/V)^2 = 16/25. 1 - 5/V = 4/5. 5/V = 1/5. V = 25.

AI explanation

Use the replacement formula: Final Quantity = Initial Quantity x (1 - Replaced Quantity / Total Volume)^n. Here, the final milk ratio is 16/25, so 16/25 = (1 - 5/V)^2. Taking the square root gives 4/5 = 1 - 5/V, which simplifies to 5/V = 1/5. Therefore, the capacity V is 25 litres.

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