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: 3115: 2116: 1718: 19

Sure, let's solve this step by step:

1. First, we need to find out the quantity of milk and water in each glass.

   • 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 and 3 parts are water. Since the glass is of 3 litres, each part is 3/5 litres. So, the quantity of milk is 2*(3/5) = 1.2 litres and the quantity of water is 3*(3/5) = 1.8 litres.

   • In the second glass, the ratio of milk to water is 3:7. This means that out of a total of 3+7=10 parts, 3 parts are milk and 7 parts are water. Since the glass is of 4 litres, each part is 4/10 litres. So, the quantity of milk is 3*(4/10) = 1.2 litres and the quantity of water is 7*(4/10) = 2.8 litres.

   • In the third glass, the ratio of milk to water is 4:11. This means that out of a total of 4+11=15 parts, 4 parts are milk and 11 parts are water. Since the glass is of 5 litres, each part is 5/15 litres. So, the quantity of milk is 4*(5/15) = 1.33 litres and the quantity of water is 11*(5/15) = 3.67 litres.

2. Now, we add up the quantities of milk and water from all the glasses:

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

3. The ratio of milk to water in the vessel is therefore 3.73:8.27. To simplify this ratio, we can multiply both sides by 100 to get rid of the decimal points, which gives us 373:827.

4. However, none of the options match this ratio. There might be a mistake in the question or the options provided.