A mixture of 40 litres of milk and water contains `10%` water. How much water should be added to this so that water may be `20%` in the new mixture?

Options

A. 4 litres
B. 5 litres
C. 6.5 litres
D. 7.5 litres

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the amount of water in the initial mixture.
The initial mixture is 40 litres, and it contains 10% water.

\[ \text{Amount of water} = 10\% \text{ of } 40 \text{ litres} = \frac{10}{100} \times 40 = 4 \text{ litres} \]

### Step 2: Determine the amount of milk in the initial mixture.
Since the total mixture is 40 litres and it contains 4 litres of water, the remaining part must be milk.

\[ \text{Amount of milk} = 40 \text{ litres} - 4 \text{ litres} = 36 \text{ litres} \]

### Step 3: Set up the equation for the new mixture.
Let \( x \) be the amount of water to be added. After adding \( x \) litres of water, the total amount of water will be \( 4 + x \) litres, and the total volume of the mixture will be \( 40 + x \) litres.

### Step 4: Set the percentage of water in the new mixture.
We want the percentage of water in the new mixture to be 20%. Therefore, we can set up the equation:

\[ \frac{4 + x}{40 + x} = 20\% \]

### Step 5: Convert the percentage to a fraction.
Convert 20% to a fraction:

\[ 20\% = \frac{20}{100} = \frac{1}{5} \]

### Step 6: Cross-multiply to solve for \( x \).
Now we can cross-multiply:

\[ 5(4 + x) = 1(40 + x) \]

Expanding both sides gives:

\[ 20 + 5x = 40 + x \]

### Step 7: Rearranging the equation.
Now, rearranging the equation to isolate \( x \):

\[ 5x - x = 40 - 20 \]

\[ 4x = 20 \]

### Step 8: Solve for \( x \).
Dividing both sides by 4 gives:

\[ x = \frac{20}{4} = 5 \]

### Conclusion:
Thus, the amount of water that should be added to the mixture is **5 litres**.

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