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The ratio of milk and water in three sam...

The ratio of milk and water in three samples is 1 : 3, 3 : 5 and 11 : 5. A mixture containing equal quantities of all three samples is made. What will be the ratio of milk and water in the new mixture?

A

`7 : 9`

B

`5 : 7`

C

`15 : 13`

D

`9 : 11`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of finding the ratio of milk and water in a new mixture made from three samples with given ratios, we will follow these steps: ### Step-by-Step Solution: 1. **Identify the Ratios**: The ratios of milk to water in the three samples are: - Sample 1: 1 : 3 - Sample 2: 3 : 5 - Sample 3: 11 : 5 2. **Convert Ratios to Quantities**: Let's assume we take an equal quantity of each sample. For simplicity, we can assume we take 16 liters from each sample (the least common multiple of the denominators in the ratios). 3. **Calculate Total Parts in Each Sample**: - For Sample 1: Total parts = 1 + 3 = 4 - For Sample 2: Total parts = 3 + 5 = 8 - For Sample 3: Total parts = 11 + 5 = 16 4. **Calculate Milk and Water in Each Sample**: - **Sample 1**: - Milk = (1/4) * 16 = 4 liters - Water = (3/4) * 16 = 12 liters - **Sample 2**: - Milk = (3/8) * 16 = 6 liters - Water = (5/8) * 16 = 10 liters - **Sample 3**: - Milk = (11/16) * 16 = 11 liters - Water = (5/16) * 16 = 5 liters 5. **Total Milk and Water in the Mixture**: - Total Milk = 4 + 6 + 11 = 21 liters - Total Water = 12 + 10 + 5 = 27 liters 6. **Calculate the Ratio of Milk to Water**: The ratio of milk to water in the new mixture is: \[ \text{Ratio} = \frac{21}{27} = \frac{7}{9} \] ### Final Answer: The required ratio of milk to water in the new mixture is **7 : 9**. ---
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