55 litres of a mixture has milk. and water in the ratio 7:4. How much water must be added to get milk and water in the ratio 7:6 in the resulting mixture.

Options

A. 16litres
B. 15litres
C. 12litres
D. 10litres

Answer

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

### Step 1: Determine the initial quantities of milk and water in the mixture.
The total volume of the mixture is 55 liters, and the ratio of milk to water is 7:4.

- Total parts = 7 (milk) + 4 (water) = 11 parts
- Quantity of milk = (7/11) * 55 = 35 liters
- Quantity of water = (4/11) * 55 = 20 liters

### Step 2: Set up the equation for the new ratio after adding water.
Let \( A \) be the amount of water added. After adding \( A \) liters of water, the new quantity of water will be \( 20 + A \) liters, while the quantity of milk remains 35 liters.

We want the new ratio of milk to water to be 7:6.

### Step 3: Write the equation based on the new ratio.
According to the new ratio:

\[ \frac{Milk}{Water} = \frac{7}{6} \]

Substituting the quantities we have:

\[ \frac{35}{20 + A} = \frac{7}{6} \]

### Step 4: Cross-multiply to solve for \( A \).
Cross-multiplying gives us:

\[ 35 \cdot 6 = 7 \cdot (20 + A) \]

This simplifies to:

\[ 210 = 140 + 7A \]

### Step 5: Isolate \( A \) and solve.
Now, we can isolate \( A \):

\[ 210 - 140 = 7A \]
\[ 70 = 7A \]
\[ A = \frac{70}{7} = 10 \]

### Conclusion:
The amount of water that must be added is **10 liters**.

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