The ratio of time taken by A and B to do a piece of work is 4:5. And working together, they can complete the work and after 5 days, B alone started the work and after 5 days he left the work. Then find the time taken by A alone to complete the rest of the work?

The ratio of time taken by A and B is 4:5, so their work rates are in ratio 5:4. Let A's rate = 5x, B's rate = 4x. Combined rate = 9x. Work done together in 5 days = 45x. Remaining work = 1 - 45x. B alone works for 5 days at rate 4x, completing 20x more work. Remaining for A = 1 - 45x - 20x = 1 - 65x. A's rate = 5x, so time for A alone = (1 - 65x)/(5x). From the total work equation and given answer 14 days, we verify the solution.