Three glasses of sizes 3 litres, 4 litres and 5 litres contain mixture of milk and water in the ratio 2: 3, 3: 7 and 4: 11, respectively. The contents of all the three glasses are poured into a single vessel. Find the ratio of milk
Question
Three glasses of sizes 3 litres, 4 litres and 5 litres contain mixture of milk and water in the ratio 2: 3, 3: 7 and 4: 11, respectively. The contents of all the three glasses are poured into a single vessel. Find the ratio of milk
Solution
Sure, let's break it down step by step:
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First, we need to find out the amount of milk and water in each glass.
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In the first glass, the ratio of milk to water is 2:3. This means that out of a total of 2+3=5 parts, 2 parts are milk. So, the amount of milk in the first glass is 2/5 * 3 litres = 1.2 litres.
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In the second glass, the ratio is 3:7. So, the amount of milk is 3/10 * 4 litres = 1.2 litres.
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In the third glass, the ratio is 4:11. So, the amount of milk is 4/15 * 5 litres = 1.33 litres.
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Now, we add up the amounts of milk from all three glasses: 1.2 litres + 1.2 litres + 1.33 litres = 3.73 litres.
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We do the same for the water:
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In the first glass, the amount of water is 3/5 * 3 litres = 1.8 litres.
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In the second glass, the amount of water is 7/10 * 4 litres = 2.8 litres.
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In the third glass, the amount of water is 11/15 * 5 litres = 3.67 litres.
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Adding up the amounts of water gives us: 1.8 litres + 2.8 litres + 3.67 litres = 8.27 litres.
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So, the ratio of milk to water in the final mixture is 3.73 litres : 8.27 litres.
To simplify this ratio, we can divide both numbers by their greatest common divisor, which is approximately 0.01. This gives us a final ratio of approximately 373:827.
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