Question

A 30 litres mixture of milk and water has 10% water. How much milk should be added so that the percentage of water in the mixture comes down to 2%?

• A. 120
• B. 80
• C. 90
• D. 60

Hint:

When working with mixtures and percentages, set up an equation based on the known and desired proportions.

Answer 1

The Correct Option is A

In the given mixture:
- The total volume is 30 litres.
- The amount of water in the mixture is \( 10% \) of 30, i.e., \( 30 \times 0.10 = 3 \) litres.
Let \( x \) be the amount of milk to be added. After adding \( x \) litres of milk, the new total volume of the mixture will be \( 30 + x \) litres.
The new percentage of water should be \( 2% \), so the amount of water in the new mixture is \( 2% \) of \( 30 + x \), i.e.,
\[ \text{Water content} = 0.02 \times (30 + x) \] We know that the water content remains the same, i.e., 3 litres, so we can set up the equation:
\[ 3 = 0.02 \times (30 + x) \] Solving for \( x \):
\[ 3 = 0.02 \times 30 + 0.02 \times x \] \[ 3 = 0.6 + 0.02x \] \[ 3 - 0.6 = 0.02x \] \[ 2.4 = 0.02x \] \[ x = \frac{2.4}{0.02} = 120 \] Thus, the amount of milk to be added is \( \boxed{120} \) litres.