How many litres of water needs to be added to 14 litres of solution, having milk and water in ratio 4 : 3, such that the resultant solution has milk and water in ratio 1 : 2?
Question
How many litres of water needs to be added to 14 litres of solution, having milk and water in ratio 4 : 3, such that the resultant solution has milk and water in ratio 1 : 2?
Solution
Sure, let's solve this step by step:
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In the initial solution, the ratio of milk to water is 4:3. This means that out of 7 parts of the solution (4 parts milk + 3 parts water), 4 parts are milk and 3 parts are water.
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So, in 14 litres of the solution, the quantity of milk is (4/7)*14 = 8 litres and the quantity of water is (3/7)*14 = 6 litres.
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We want to add some water to this solution so that the ratio of milk to water becomes 1:2. This means that the quantity of milk (which remains 8 litres as we are not adding any milk) should be one-third of the quantity of water in the new solution.
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Let's denote the quantity of water to be added as x litres. So, the total quantity of water in the new solution will be 6 litres (existing) + x litres (added).
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According to the new ratio 1:2, we have 8 litres of milk = 1/3 * (6 + x) litres of water.
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Solving this equation for x gives us x = 18 litres.
So, 18 litres of water needs to be added to the solution to get the desired ratio.
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