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

To solve this problem, we need to find the amount of milk and water in each glass and then add them together.

1. In the first glass, the ratio of milk to water is 2:3. This means that 2/5 of the mixture is milk and 3/5 is water. So, the amount of milk is 2/5 * 3 litres = 1.2 litres and the amount of water is 3/5 * 3 litres = 1.8 litres.

2. In the second glass, the ratio of milk to water is 3:7. This means that 3/10 of the mixture is milk and 7/10 is water. So, the amount of milk is 3/10 * 4 litres = 1.2 litres and the amount of water is 7/10 * 4 litres = 2.8 litres.

3. In the third glass, the ratio of milk to water is 4:11. This means that 4/15 of the mixture is milk and 11/15 is water. So, the amount of milk is 4/15 * 5 litres = 1.333 litres and the amount of water is 11/15 * 5 litres = 3.667 litres.

Now, we add the amounts of milk and water together:

Total milk = 1.2 litres + 1.2 litres + 1.333 litres = 3.733 litres Total water = 1.8 litres + 2.8 litres + 3.667 litres = 8.267 litres

The ratio of milk to the total mixture is 3.733 litres / (3.733 litres + 8.267 litres) = 0.311 or approximately 31.1%.

So, the ratio of milk to water in the final mixture is approximately 31:69, which is not one of the options given. There might be a mistake in the problem or the options.

To solve this problem, we need to find the amount of milk and water in each glass and then add them together.

1. In the first glass, the ratio of milk to water is 2:3. This means that 2/5 of the mixture is milk and 3/5 is water. So, the amount of milk is 2/5 * 3 litres = 1.2 litres and the amount of water is 3/5 * 3 litres = 1.8 litres.

2. In the second glass, the ratio of milk to water is 3:7. This means that 3/10 of the mixture is milk and 7/10 is water. So, the amount of milk is 3/10 * 4 litres = 1.2 litres and the amount of water is 7/10 * 4 litres = 2.8 litres.

3. In the third glass, the ratio of milk to water is 4:11. This means that 4/15 of the mixture is milk and 11/15 is water. So, the amount of milk is 4/15 * 5 litres = 1.33 litres and the amount of water is 11/15 * 5 litres = 3.67 litres.

Now, we add the amounts of milk and water together:

Total milk = 1.2 litres + 1.2 litres + 1.33 litres = 3.73 litres Total water = 1.8 litres + 2.8 litres + 3.67 litres = 8.27 litres

The ratio of milk to the total mixture is 3.73 litres / (3.73 litres + 8.27 litres) = 0.31

So, the ratio of milk to water in the final mixture is approximately 31:69, which is not listed in the options. There might be a mistake in the problem or the options.