A mixture of water and milk is 40 litres. There is 10%.water in it. How much water should now be added in this mixture so that the new mixture contains 20% water? 

Options

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

Answer

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

### Step 1: Determine the amount of water in the original mixture.
The total volume of the mixture is 40 liters, and it contains 10% water.

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

### Step 2: Define the variables.
Let \( x \) be the amount of water to be added to the mixture. After adding \( x \) liters of water, the total amount of water in the mixture will be \( 4 + x \) liters.

### Step 3: Determine the new total volume of the mixture.
After adding \( x \) liters of water, the new total volume of the mixture will be:

\[ \text{Total volume} = 40 + x \text{ liters} \]

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

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

Converting 20% to a fraction gives us:

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

So, we rewrite the equation:

\[ \frac{4 + x}{40 + x} = \frac{1}{5} \]

### Step 5: Cross-multiply to solve for \( x \).
Cross-multiplying gives us:

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

Expanding both sides:

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

### Step 6: Rearranging the equation.
Now, we will rearrange the equation to isolate \( x \):

\[ 20 + 5x - x = 40 \]
\[ 20 + 4x = 40 \]
\[ 4x = 40 - 20 \]
\[ 4x = 20 \]

### Step 7: Solve for \( x \).
Dividing both sides by 4 gives:

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

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

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