In a 729 litres mixture of milk and water, the ratio of milk to water is 7:2. To get a new mixture containing milk and water in the ratio 7:3, the amount of water to be added is

Options

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres

Answer

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

### Step 1: Determine the quantities of milk and water in the original mixture.
The total volume of the mixture is 729 litres, and the ratio of milk to water is 7:2.

- The total parts in the ratio = 7 + 2 = 9 parts.
- Quantity of milk = (7/9) * 729 litres = 567 litres.
- Quantity of water = (2/9) * 729 litres = 162 litres.

### Step 2: Set up the equation for the new mixture.
We need to find the amount of water (let's call it x litres) to be added to achieve a new ratio of milk to water of 7:3.

- The quantity of milk remains the same at 567 litres.
- The new quantity of water = 162 litres + x litres.

### Step 3: Write the equation based on the new ratio.
According to the new ratio of milk to water (7:3), we can set up the equation:

\[ \frac{567}{162 + x} = \frac{7}{3} \]

### Step 4: Cross-multiply to solve for x.
Cross-multiplying gives us:

\[ 7(162 + x) = 3(567) \]

Expanding both sides:

\[ 1134 + 7x = 1701 \]

### Step 5: Solve for x.
Now, isolate x:

\[ 7x = 1701 - 1134 \]
\[ 7x = 567 \]
\[ x = \frac{567}{7} = 81 \]

### Conclusion:
The amount of water to be added is **81 litres**.

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