Deepak alone can whitewash a community hall in 33 days and Eshwar alone in 22 days. They work on alternate days, Deepak taking the first day. How long does the hall take?

Take the hall as 66 units: Deepak 2/day, Eshwar 3/day, so a Deepak-then-Eshwar pair yields 5 units. Thirteen pairs — 26 days — give 65 units. Day 27 is Deepak's, and he needs only 1 of his 2 units, so he finishes halfway through it: 26.5 days. 26 days stops at the last complete pair with 1 unit still undone. 27 days charges a whole day for that final half. 26.4 days averages the pair into a steady 2.5 units a day (66 ÷ 2.5), which ignores that the closing day is worked by the slower of the two.