132 litres of a mixture contains milk and water in the ratio 8:3.How much water must be added to the mixture so as to make the ratio of milk and water 2:1?12 litres14 litres16 litres20 litres
Question
132 litres of a mixture contains milk and water in the ratio 8:3.How much water must be added to the mixture so as to make the ratio of milk and water 2:1?12 litres14 litres16 litres20 litres
Solution
The initial volume of the mixture is 132 litres, with milk and water in the ratio 8:3.
Step 1: Find the initial volumes of milk and water. The total parts of the mixture = 8 parts milk + 3 parts water = 11 parts. So, 1 part of the mixture = 132 litres / 11 = 12 litres. Therefore, the volume of milk = 8 parts * 12 litres/part = 96 litres. And the volume of water = 3 parts * 12 litres/part = 36 litres.
Step 2: Determine how much water to add to make the ratio 2:1. In the new mixture, the ratio of milk to water should be 2:1. Since the volume of milk remains constant at 96 litres, this represents 2 parts in the new ratio. So, 1 part in the new ratio = 96 litres / 2 = 48 litres. Therefore, the volume of water in the new ratio should be = 1 part * 48 litres/part = 48 litres.
Step 3: Calculate the amount of water to be added. The amount of water to be added = Final volume of water - Initial volume of water = 48 litres - 36 litres = 12 litres.
So, 12 litres of water must be added to the mixture to make the ratio of milk and water 2:1.
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