Multiple choice

From a vessel containing 60 litres of pure wine, 4 litres are drawn out and replaced by water. 4 litres of the mixture is again drawn out and replaced with water. What is the ratio of wine to water in the resultant mixture?

  1. 4 : 3

  2. 17 : 4

  3. 196 : 29

  4. 21 : 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wine remaining = Initial * (1 - 4/60)^2 = 60 * (56/60)^2 = 60 * (14/15)^2 = 60 * 196/225 = 196/3.75 = 52.266. Water = 60 - 52.266 = 7.733. Ratio = 52.266 : 7.733 = 196 : 29.

AI explanation

Using the replacement formula, the final quantity of wine is calculated as Initial Volume multiplied by (1 minus Replacement Volume divided by Total Volume) to the power of the number of operations. This gives 60 multiplied by (1 minus 4 divided by 60) squared, equaling 60 multiplied by the fraction 14 over 15 squared, which results in 392 over 5 litres of wine. The remaining volume in the vessel is water, which is 60 minus 392 over 5, equaling 58 over 5 litres, making the required ratio 196 to 29.

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