Discussion
A softener treats water of 200 milligrams per litre hardness to 5 milligrams per litre. What percentage of the hardness is removed?
Answer: C
Correct answer: 97.5 per cent
\[ \frac{200-5}{200} = \frac{195}{200} = 0.975 = 97.5\%. \] The base is the hardness entering, so the removal is 97.5 per cent. The 2.5 per cent offered is the fraction *remaining*, which is the same calculation read the wrong way round, and 5 mg/L is a normal softener outlet figure for textile use.
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