In a 3 litre mixture of water and milk, 50% is milk. How much water should be added so that the percentage of milk becomes 20%?

Options

A. 1.5 litre
B. 4.5 litre
C. 2.5 litre
D. 3 litre

Answer

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

**Step 1: Determine the amount of milk in the mixture.**
- The total volume of the mixture is 3 liters.
- Since 50% of the mixture is milk, the amount of milk is:
\[ \text{Amount of milk} = 50\% \text{ of } 3 \text{ liters} = \frac{50}{100} \times 3 = 1.5 \text{ liters} \]

**Step 2: Let the amount of water to be added be \( x \) liters.**
- After adding \( x \) liters of water, the total volume of the mixture becomes:
\[ \text{Total volume} = 3 + x \text{ liters} \]

**Step 3: Set up the equation for the percentage of milk.**
- We want the percentage of milk in the new mixture to be 20%. The equation for the percentage of milk is:
\[ \frac{\text{Amount of milk}}{\text{Total volume}} \times 100 = 20 \]
- Plugging in the values we have:
\[ \frac{1.5}{3 + x} \times 100 = 20 \]

**Step 4: Solve the equation for \( x \).**
- First, simplify the equation:
\[ \frac{1.5}{3 + x} = \frac{20}{100} = 0.2 \]
- Cross-multiplying gives:
\[ 1.5 = 0.2(3 + x) \]
- Expanding the right side:
\[ 1.5 = 0.6 + 0.2x \]
- Subtracting 0.6 from both sides:
\[ 1.5 - 0.6 = 0.2x \]
\[ 0.9 = 0.2x \]
- Dividing both sides by 0.2:
\[ x = \frac{0.9}{0.2} = 4.5 \]

**Final Answer:**
- The amount of water that should be added is \( 4.5 \) liters.

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