Q: 19 of 30 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. Options : 14: 31 15: 21 16: 17 18: 19
Question
Q: 19 of 30 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.
Options : 14: 31 15: 21 16: 17 18: 19
Solution
The problem involves finding the ratio of milk to water in a mixture that comes from combining the contents of three glasses with different ratios of milk to water. Here's how to solve it:
Step 1: Find the amount of milk and water in each glass.
For the first glass: The ratio of milk to water is 2:3, which means for every 2 parts of milk, there are 3 parts of water. Since the glass is 3 litres, each part is 3/(2+3) = 0.6 litres. So, the amount of milk is 20.6 = 1.2 litres and the amount of water is 30.6 = 1.8 litres.
For the second glass: The ratio of milk to water is 3:7. Each part is 4/(3+7) = 0.4 litres. So, the amount of milk is 30.4 = 1.2 litres and the amount of water is 70.4 = 2.8 litres.
For the third glass: The ratio of milk to water is 4:11. Each part is 5/(4+11) = 0.3125 litres. So, the amount of milk is 40.3125 = 1.25 litres and the amount of water is 110.3125 = 3.4375 litres.
Step 2: Add up the amounts of milk and water from all glasses.
Total amount of milk = 1.2 + 1.2 + 1.25 = 3.65 litres Total amount of water = 1.8 + 2.8 + 3.4375 = 8.0375 litres
Step 3: Find the ratio of milk to water in the combined mixture.
The ratio of milk to water is 3.65 : 8.0375. To simplify this ratio, we can divide both numbers by their greatest common divisor. In this case, it's easier to multiply both sides by 100 to get rid of the decimal places, resulting in 365 : 803.75.
However, none of the given options match this ratio. There might be a mistake in the problem or the options.
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