Question
A 30-litre mixture consists of milk and water in the
ratio of 5:7. To this mixture, 2.5 litres of milk and 4.5 litres of water are added. How much more needs to be added to achieve a final mixture where the milk-to-water ratio is 3:5?Solution
Quantity of milk in 30 litres of initial mixture = (5/12) X 30 = 12.5 litres
Quantity of water in 30 litres of initial mixture = (7/12) X 30 = 17.5 litres
After adding more components,
Quantity of milk = 12.5 + 2.5 = 15 litres
Quantity of water = 17.5 + 4.5 = 22 litres
Let 'x' litres of milk and 'y' litres of water are required to be added to obtain a mixture containing milk and water in the ratio 3∶ 5
=> (15 + x)/(22 + y) = 3/5
=> 75 + 5x = 66 + 3y
=> 3y - 5x = 9
Putting x = 0,
=> y = 9/3 = 3
∴ The desired ratio can be obtained by adding 3 litres of water
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