Question
The ratio of the milk to water in a mixture is 9:4. 39 litres of mixture is removed and 13 litres of water is added. If in the resulting mixture, the milk is double the water, find the quantity of water in the initial mixture.
Solution
Let the quantity of the milk in the initial mixture = 9x litres
The quantity of the water in the initial mixture = 4x litres
The quantity of milk in 39 litres of mixture = (39/13) × 9 = 27 litres
The quantity of water in 39 litres of mixture = (39/13) × 4 = 12 litres
According to the question,
(9x – 27) = 2 × (4x – 12 + 13)
9x – 27 = 2 × (4x + 1)
9x – 27 = 8x + 2
x = 29
The quantity of water in the initial mixture = 4 × 29 = 116 litres
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