A and B work together, to complete a job in 15 days. If A complete half of the work alone and B complete half of the remaining work. The work will be complete in 40 days. Find the difference between the time taken by A and B to complete this work alone ?

Let A take a days, B take b days alone. Together: 1/a + 1/b = 1/15. In the scenario, A does half work (a/2 days), B does remaining half (b/2 days): a/2 + b/2 = 40, so a + b = 80. From combined rate: (a + b)/ab = 1/15, so ab = 15(a + b) = 1200. Solving a + b = 80 and ab = 1200 gives a = 20, b = 60. Difference = |60 - 20| = 40 days.