In a mixture of 45 litres, the ratio of milk and water is 3 : 2. How much water must be added to make the ratio 9 : 11?

Options

A. 10 litres
B. 15 litres
C. 17 litres
D. 20 litres

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the initial quantities of milk and water.
The total mixture is 45 liters with a ratio of milk to water as 3:2.

To find the quantities of milk and water, we can use the ratio:
- Total parts in the ratio = 3 + 2 = 5 parts.
- Each part represents = Total mixture / Total parts = 45 liters / 5 = 9 liters.

Now we can find the quantities:
- Milk = 3 parts = 3 * 9 = 27 liters.
- Water = 2 parts = 2 * 9 = 18 liters.

### Step 2: Set up the equation for the new ratio after adding water.
We need to find how much water (let's call it x liters) must be added to change the ratio of milk to water to 9:11.

After adding x liters of water, the new quantity of water will be:
- New water quantity = 18 liters + x liters.

### Step 3: Write the equation based on the new ratio.
According to the new ratio of milk to water (9:11):
\[ \frac{27}{18 + x} = \frac{9}{11} \]

### Step 4: Cross-multiply to solve for x.
Cross-multiplying gives us:
\[ 27 * 11 = 9 * (18 + x) \]
\[ 297 = 162 + 9x \]

### Step 5: Solve for x.
Now, isolate x:
\[ 297 - 162 = 9x \]
\[ 135 = 9x \]
\[ x = \frac{135}{9} = 15 \]

### Conclusion:
The amount of water that must be added is **15 liters**.

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