A dishonest milk man mixed 1 liter of water for every 3 liters of milk and thus made up 36 liters of milk. If he now adds 15 liters of milk to mixture, find the ratio of milk and water in the new mixture:

Options

A. `12 : 5`
B. `14 : 3`
C. `7 : 2`
D. `9 : 4`

Answer

To solve the problem step by step, we will first determine the initial quantities of milk and water in the mixture, and then we will find the new ratio after adding more milk.

### Step 1: Determine the initial quantities of milk and water.
The milkman mixes 1 liter of water for every 3 liters of milk. Therefore, the total parts of the mixture can be represented as:

- Milk = 3 parts
- Water = 1 part

This gives us a total of 3 + 1 = 4 parts.

### Step 2: Calculate the quantity of milk and water in the 36 liters mixture.
Since the total mixture is 36 liters, we can find the quantity of each component using the ratio:

- Quantity of milk = (3 parts / 4 parts) * 36 liters = 27 liters
- Quantity of water = (1 part / 4 parts) * 36 liters = 9 liters

### Step 3: Add the additional milk to the mixture.
The milkman adds 15 liters of milk to the existing mixture. Therefore, the new quantity of milk becomes:

- New quantity of milk = 27 liters (initial milk) + 15 liters (added milk) = 42 liters

### Step 4: Determine the total quantity of water in the mixture.
The quantity of water remains unchanged at 9 liters since no water was added.

### Step 5: Find the new ratio of milk to water.
Now we can find the ratio of milk to water in the new mixture:

- Ratio of milk to water = Quantity of milk : Quantity of water = 42 liters : 9 liters

### Step 6: Simplify the ratio.
To simplify the ratio, we can divide both sides by their greatest common divisor (GCD). The GCD of 42 and 9 is 3.

- Simplified ratio = (42 ÷ 3) : (9 ÷ 3) = 14 : 3

Thus, the final ratio of milk to water in the new mixture is **14:3**.

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