A vat holds 60 litres of sugarcane juice in which the sugar makes up 10% of the volume. How many litres of water must be boiled off so that the sugar comes to 15% of what is left?

Boiling drives off water only, so the sugar stays fixed at 10% of 60 = 6 litres. For 6 litres to be 15% of the vat, the vat must hold 6/0.15 = 40 litres, so 60 − 40 = 20 litres must go. (40 is what REMAINS, not what is driven off. 6 is the sugar itself, which never changes. And measuring the 5-point rise against the original 10% — 'half as much again, so remove half' — gives 30 litres, which would leave the juice at 6/30 = 20% sugar, too strong.)