Sohan, Tarun and Umesh can each finish a carpentry job on their own in 16, 24 and 48 days respectively. All three start together, but at the end of the fourth day the quickest of them is called away to another site. How many further days do the other two need?

Take the job as 48 units: Sohan 3/day, Tarun 2/day, Umesh 1/day, so all three give 6 units a day. Four days put in 24 units, leaving 24. Sohan is the quickest and leaves, so Tarun and Umesh carry on at 2 + 1 = 3 units a day: 24 ÷ 3 = 8 more days. 4 days is what would remain if all three stayed (48 ÷ 6 = 8 days in all). 12 days leaves Tarun to finish alone (24 ÷ 2), forgetting Umesh. 24 days leaves Umesh alone (24 ÷ 1), forgetting Tarun.