Naveen alone can compile a report in 24 days and Om alone in 36 days. They compile it on alternate days with Naveen taking the first day. How long does the report take?

Take the report as 72 units: Naveen 3/day, Om 2/day, so a Naveen-then-Om pair yields 5 units. Fourteen pairs — 28 days — give 70 units. Day 29 is Naveen's, and he needs only 2 of his 3 units, so he finishes two-thirds of the way through it: 28 2/3 days. 29 days is what it would take if Om had started, since his 2 units would exactly close the report on day 29 — the order matters. 28.8 days averages the pair into a steady 2.5 units a day (72 ÷ 2.5). 30 days rounds up to a whole further pair of days.