The ratio of milk and water in 55 litres of adulterated milk is `7 : 4`. How much water must be added to make the mixture's ratio `7 : 6`?

Options

A. 5 l
B. 10 l
C. 15 l
D. 25 l

Answer

To solve the problem step by step, we need to determine how much water must be added to a mixture of milk and water to change the ratio from 7:4 to 7:6.

### Step 1: Determine the total parts in the initial ratio.
The initial ratio of milk to water is 7:4.
- Total parts = 7 + 4 = 11 parts.

**Hint:** Always add the parts of the ratio to find the total.

### Step 2: Calculate the volume of milk and water in the mixture.
Given that the total volume of the mixture is 55 liters:
- Volume of milk = (7/11) * 55 = 35 liters.
- Volume of water = (4/11) * 55 = 20 liters.

**Hint:** Use the formula (part/total parts) * total volume to find the individual volumes.

### Step 3: Set up the equation for the new ratio.
Let \( x \) be the amount of water to be added. After adding \( x \) liters of water, the new volume of water becomes \( 20 + x \) liters. The volume of milk remains 35 liters.

We need to set the new ratio of milk to water to be 7:6:
\[ \frac{35}{20 + x} = \frac{7}{6} \]

**Hint:** When changing ratios, set up a proportion to find the unknown.

### Step 4: Cross-multiply to solve for \( x \).
Cross-multiplying gives:
\[ 35 \cdot 6 = 7 \cdot (20 + x) \]
\[ 210 = 140 + 7x \]

**Hint:** Cross-multiplication helps eliminate the fraction for easier solving.

### Step 5: Isolate \( x \).
Subtract 140 from both sides:
\[ 210 - 140 = 7x \]
\[ 70 = 7x \]
Now, divide both sides by 7:
\[ x = 10 \]

**Hint:** Isolate the variable by performing inverse operations.

### Conclusion:
To achieve the new ratio of 7:6, we need to add **10 liters** of water.

**Final Answer:** 10 liters.