A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in

Rate of work by A = 1/9
Rate of work by B = 1/12
A works on first day and B works on second day.Hence in two days the amount of work done = (1/9) + (1/12) = 7/36
In 10 days the amount of work done = 35/36.
A would start working on the 11th day and needs to finish 1/36 th of the work.
Since A completes 1/9 th of the total work in a day , it would take him 1/4th of the day to complete 1/36 th of the work.
Total time taken is 10 days and 1/4 th of the 11 th day.
Hence Option C is the correct answer.