A school's attendance rose from 84% of its strength on Monday to 90% of its strength on Tuesday, the strength being unchanged. If 96 pupils were absent on Monday, how many were absent on Tuesday?

Work with the absentees, not the attendees. On Monday 100 - 84 = 16% of the strength were away, so 0.16 $x$ strength = 96 and the strength is 600. On Tuesday 100 - 90 = 10% were away: 10% of 600 = 60. 90 subtracts the 6-point gap as though it meant 6 pupils. 86 cuts 96 by 10%, using the attendance rate as though it were a fall in absentees. 54 is $96\times 9/16$, scaling by the PRESENT share of 90 where the ABSENT share of 10 belongs.