20 litres of a mixture contains milk and water in the ratio 5:3 . If 4 litres of this mixture be replaced by 4 litres of milk , the ratio of milk to water in the new mixture would be :

Options

A. `2:1`
B. `7:3`
C. `8:3`
D. `4:3`

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Determine the initial quantities of milk and water in the mixture.

The total volume of the mixture is 20 liters, and the ratio of milk to water is 5:3.

To find the quantity of milk and water, we first calculate the total parts in the ratio:
- Total parts = 5 (milk) + 3 (water) = 8 parts.

Now, we can find the quantity of milk and water:
- Quantity of milk = (5/8) * 20 = 12.5 liters.
- Quantity of water = (3/8) * 20 = 7.5 liters.

### Step 2: Calculate the amount of milk and water removed when 4 liters of the mixture is taken out.

Since the mixture is in the ratio of 5:3, we will find out how much milk and water is in the 4 liters removed:
- Milk in 4 liters = (5/8) * 4 = 2.5 liters.
- Water in 4 liters = (3/8) * 4 = 1.5 liters.

### Step 3: Update the quantities of milk and water after removing 4 liters of the mixture.

Now we will subtract the quantities of milk and water removed from the original quantities:
- Remaining milk = 12.5 - 2.5 = 10 liters.
- Remaining water = 7.5 - 1.5 = 6 liters.

### Step 4: Add 4 liters of milk to the remaining mixture.

Next, we add 4 liters of milk to the remaining mixture:
- New quantity of milk = 10 + 4 = 14 liters.
- Quantity of water remains the same = 6 liters.

### Step 5: Calculate the new ratio of milk to water.

Now, we can find the new ratio of milk to water:
- Ratio of milk to water = 14:6.

To simplify this ratio, we divide both sides by 2:
- Simplified ratio = 7:3.

### Final Answer:
The ratio of milk to water in the new mixture is **7:3**.

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