In 729 ml mixture the ratio of milk and water is 7.2. How much quantity of water should be added in new mixture so that the ratio of milk and water becomes 7:3?

Options

A. 72 ml
B. 81 ml
C. 85 ml
D. 90 ml

Answer

To solve the problem, we need to find out how much water should be added to a mixture of milk and water so that the new ratio of milk to water becomes 7:3. Here’s a step-by-step solution:

### Step 1: Understand the initial mixture
The total volume of the mixture is 729 ml, and the ratio of milk to water is 7:2.

### Step 2: Calculate the total parts in the ratio
The total parts in the ratio of milk to water (7:2) is:
\[ 7 + 2 = 9 \text{ parts} \]

### Step 3: Calculate the quantity of milk and water in the initial mixture
To find the quantity of milk and water, we can use the total volume and the ratio:
- Quantity of milk:
\[ \text{Milk} = \frac{7}{9} \times 729 = 567 \text{ ml} \]
- Quantity of water:
\[ \text{Water} = \frac{2}{9} \times 729 = 162 \text{ ml} \]

### Step 4: Set up the equation for the new ratio
We want the new ratio of milk to water to be 7:3. Let \( x \) be the amount of water we need to add. The new quantity of water will be:
\[ 162 + x \text{ ml} \]

### Step 5: Write the equation for the new ratio
The new ratio of milk to water can be expressed as:
\[ \frac{567}{162 + x} = \frac{7}{3} \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 3 \times 567 = 7 \times (162 + x) \]
\[ 1701 = 1134 + 7x \]

### Step 7: Isolate \( x \)
Now, isolate \( x \):
\[ 1701 - 1134 = 7x \]
\[ 567 = 7x \]
\[ x = \frac{567}{7} = 81 \text{ ml} \]

### Conclusion
Thus, the quantity of water that should be added to the mixture is **81 ml**.

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