Athiya and Dean can do a piece of work in 30 days, while Dean and Cathy does the same work in 24 days. Athiya and Cathy can complete the same work in 20 days. They all work for 10 days and then, Dean and Cathy leave. How many more days will Athiya take to finish the work?

The combined daily work rate of Athiya, Dean, and Cathy is half of (1/30 + 1/24 + 1/20), which is 1/16. In 10 days, they complete 10/16 = 5/8 of the work, leaving 3/8 of the work remaining. Athiya's individual daily work rate is 1/16 - 1/24 = 1/48, meaning she would take 48 days to do the whole work alone; thus, she needs 48 * (3/8) = 18 more days to finish the remaining work.