Discussion
A 40-litre mixture of milk and water contains 10% water. How much water must be added to make the water 20% of the new mixture?
Answer: B
Correct answer: 5 litres
The mixture contains \( 40 \times 0.10 = 4 \) litres of water and 36 litres of milk. The milk is unchanged by adding water, so work from it. If water is to be 20% of the new mixture, milk must be 80%, and \[ 36 = 0.80 \times \text{new total} \;\Rightarrow\; \text{new total} = \frac{36}{0.8} = 45 \text{ litres}. \] The water to add is therefore \[ 45 - 40 = 5 \text{ litres}. \] Checking: 45 litres containing 9 of water is 20% water, and \( 9 - 4 = 5 \) litres were added. The method to carry away is to anchor on the quantity that does not change and express the target percentage in terms of it rather than of the component being added. Working forwards from the water - asking what makes 4 litres into 20% - gives 20 litres total and the wrong answer, because it ignores that the added water also enlarges the total.
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