Two vessels contain milk and water in the ratio `7:8 and 13:5`. If both vessel are mixed in ratio `1:1`, find the ratio of milk and water in new mixture?

Options

A. `107:73`
B. `105:59`
C. `111:69`
D. `103:77`

Answer

To find the ratio of milk and water in the new mixture when two vessels are mixed, we can follow these steps:

### Step 1: Identify the ratios of milk and water in each vessel.
- Vessel 1 has milk and water in the ratio of 7:8.
- Vessel 2 has milk and water in the ratio of 13:5.

### Step 2: Calculate the total parts for each vessel.
- For Vessel 1: Total parts = 7 (milk) + 8 (water) = 15 parts.
- For Vessel 2: Total parts = 13 (milk) + 5 (water) = 18 parts.

### Step 3: Determine the amount of milk and water in each vessel.
Assume we take 90 parts from Vessel 1 and 108 parts from Vessel 2 for easier calculation (the least common multiple of 15 and 18 is 90).

- For Vessel 1:
- Milk = (7/15) * 90 = 42 parts
- Water = (8/15) * 90 = 48 parts

- For Vessel 2:
- Milk = (13/18) * 90 = 65 parts
- Water = (5/18) * 90 = 25 parts

### Step 4: Combine the amounts of milk and water from both vessels.
- Total milk = 42 (from Vessel 1) + 65 (from Vessel 2) = 107 parts
- Total water = 48 (from Vessel 1) + 25 (from Vessel 2) = 73 parts

### Step 5: Write the final ratio of milk to water in the new mixture.
The ratio of milk to water in the new mixture is:
\[ \text{Ratio of milk to water} = 107 : 73 \]

### Final Answer:
The ratio of milk and water in the new mixture is **107:73**.

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