480 ml of a mixture contains milk and water in the ratio 4 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 4 : 3 ?
Question
480 ml of a mixture contains milk and water in the ratio 4 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 4 : 3 ?
Solution
In the initial mixture, the ratio of milk to water is 4:2, which simplifies to 2:1. This means that 2/3 of the mixture is milk and 1/3 is water.
So, the initial volume of water in the mixture is 480 * (1/3) = 160 ml.
In the new mixture, the ratio of milk to water should be 4:3. This means that 4/7 of the mixture is milk and 3/7 is water.
Since the amount of milk remains the same in the new mixture, we can set up the following equation to find the total volume (V) of the new mixture:
V * (4/7) = 480 * (2/3)
Solving for V gives:
V = 480 * (2/3) / (4/7) = 560 ml.
So, the volume of water to be added is the volume of water in the new mixture minus the initial volume of water:
Water to be added = V * (3/7) - 160 = 560 * (3/7) - 160 = 240 - 160 = 80 ml.
Therefore, 80 ml of water is to be added to get the new mixture.
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