A solution of milk and water contains milk and water in the ratio of 3 : 2. Another soution of milk and water contains milk and waterin the ratio of 2 : 1. Forty litres of the first solution is mixed with 30 litre of the second solution. The ratio of milk and water in the resultant solution is:

Options

A. `22:13 `
B. `13:22 `
C. `6:5 `
D. `5:6 `

Answer

To solve the problem step by step, we will first analyze the two solutions of milk and water, calculate the amounts of milk and water in each solution, and then find the ratio in the resultant mixture.

### Step 1: Understand the first solution
The first solution has milk and water in the ratio of 3:2. This means that for every 5 parts of the solution, 3 parts are milk and 2 parts are water.

- Total parts = 3 (milk) + 2 (water) = 5 parts
- Milk in the first solution = (3/5) of the total solution
- Water in the first solution = (2/5) of the total solution

### Step 2: Calculate the amount of milk and water in the first solution
We are given 40 liters of the first solution.

- Amount of milk in the first solution = (3/5) * 40 = 24 liters
- Amount of water in the first solution = (2/5) * 40 = 16 liters

### Step 3: Understand the second solution
The second solution has milk and water in the ratio of 2:1. This means that for every 3 parts of the solution, 2 parts are milk and 1 part is water.

- Total parts = 2 (milk) + 1 (water) = 3 parts
- Milk in the second solution = (2/3) of the total solution
- Water in the second solution = (1/3) of the total solution

### Step 4: Calculate the amount of milk and water in the second solution
We are given 30 liters of the second solution.

- Amount of milk in the second solution = (2/3) * 30 = 20 liters
- Amount of water in the second solution = (1/3) * 30 = 10 liters

### Step 5: Combine the two solutions
Now, we will combine the amounts of milk and water from both solutions.

- Total milk = Milk from first solution + Milk from second solution
= 24 liters + 20 liters = 44 liters

- Total water = Water from first solution + Water from second solution
= 16 liters + 10 liters = 26 liters

### Step 6: Find the ratio of milk to water in the resultant solution
Now we have:
- Total milk = 44 liters
- Total water = 26 liters

To find the ratio of milk to water, we write it as:
Ratio = Milk : Water = 44 : 26

### Step 7: Simplify the ratio
To simplify the ratio, we can divide both sides by their greatest common divisor (GCD), which is 2.

- Simplified ratio = (44/2) : (26/2) = 22 : 13

### Final Answer
The ratio of milk to water in the resultant solution is **22 : 13**.

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