Question
The ratio of the milk to water in a mixture is 11:4. 45 litres of mixture is removed and 9 litres of water is added in the remaining mixture. If in the final mixture the quantity of milk is double the quantity of water, then find the quantity of water in the initial mixture.
Solution
Let the quantity of the milk in the initial mixture = 11x litres
The quantity of the water in the initial mixture = 4x litres
The quantity of milk in 45 litres of mixture = (45/15) × 11 = 33 litres
The quantity of water in 45 litres of mixture = (45/15) × 4 = 12 litres
According to the question,
(11x – 33) = 2 × (4x – 12 + 9)
11x – 33 = 2 × (4x – 3)
11x – 33 = 8x – 6
3x = 27
x = 9
The quantity of water in the initial mixture = 4 × 9 = 36 litres
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